identifying the diffusion coefficient by optimization from the final observation this paper deals with the inverse problem of determining a pair a u in the reaction diffusion equationu t au x x f x t with initial and boundary conditionsu x 0 email protected x u x x 0 u x x 1 0 from the final measurement data u x t z x which has important application in a large fields of applied science based on the optimal control framework the existence uniqueness and stability of the minimizer for the cost functional are established a necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced the gradient iteration algorithm is applied to the inverse problem and some numerical results are presented for various typical test examples

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

determining surface temperatures from interior observations we consider the inverse heat transfer problem for the case of the one dimensional heat equation in a quarter plane and present a new solution algorithm together with error bounds of logarithmic convexity type our method is based on regularizing the initial value problem for the heat equation run sideways we describe a numerical experiment with rapidly varying temperature profiles and explain how the method can be extended to problems with temperature dependent thermal properties

direct numerical method for an inverse problem of a parabolic partial differential equation a coefficient inverse problem of the one dimensional parabolic equation is solved by a high order compact finite difference method in this paper the problem of recovering a time dependent coefficient in a parabolic partial differential equation has attracted considerable attention recently while many theoretical results regarding the existence and uniqueness of the solution are obtained the development of efficient and accurate numerical methods is still far from satisfactory in this paper a fourth order efficient numerical method is proposed to calculate the function u x t and the unknown coefficient a t in a parabolic partial differential equation several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method

the use of chebyshev cardinal functions for the solution of a partial differential equation with an unknown time dependent coefficient subject to an extra measurement a numerical technique is presented for the solution of a parabolic partial differential equation with a time dependent coefficient subject to an extra measurement the method is derived by expanding the required approximate solution as the elements of chebyshev cardinal functions using the operational matrix of derivative the problem can be reduced to a set of algebraic equations from the computational point of view the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is efficient to use

computations of two fluid models based on a simple and robust hybrid primitive variable riemann solver with ausmd this paper is to continue our previous work in 2008 on solving a two fluid model for compressible liquid gas flows we proposed a pressure velocity based diffusion term original derived from ausmd scheme of wada and liou in 1997 to enhance its robustness the proposed ausmd schemes have been applied to gas and liquid fluids universally to capture fluid discontinuities such as the fluid interfaces and shock waves accurately for the ransom s faucet problem air water shock tube problems and 2d shock water liquid interaction problems however the proposed scheme failed at computing liquid gas interfaces in problems under large ratios of pressure density and volume of fraction the numerical instability has been remedied by chang and liou in 2007 using the exact riemann solver to enhance the accuracy and stability of numerical flux across the liquid gas interface here instead of the exact riemann solver we propose a simple ausmd type primitive variable riemann solver pvrs which can successfully solve 1d stiffened water air shock tube and 2d shock gas interaction problems under large ratios of pressure density and volume of fraction without the expensive cost of tedious computer time in addition the proposed approach is shown to deliver a good resolution of the shock front rarefaction and cavitation inside the evolution of high speed droplet impact on the wall

unified graph based multi fluid model for gas liquid pipeline flows we present a novel model of transient multiphase flow for gas liquid mixtures in long pipelines the study develops a general flexible formulation of a one dimensional flow for complex multiphase mixtures in the presence of slip and mass exchange multi fluid and drift flux approaches are combined the multi fluid model governs the momentum balance for the fluids and drift flux correlations are used for modelling of the slip between individual components a tree like graph is introduced to describe the hierarchy of fluids and components within the mixture the numerical implementation for an arbitrary number of components is based on the extension of the semi implicit method for pressure linked equations imbalances of equations are selected as criteria for iteration convergence specific corrections are discussed including those proposed for the equilibrium gas release model

spectral regularization method for a cauchy problem of the time fractional advection dispersion equation in this paper a cauchy problem for the time fractional advection dispersion equation tfade is investigated such a problem is obtained from the classical advection dispersion equation by replacing the first order time derivative by the caputo fractional derivative of order a 0 a 1 we show that the cauchy problem of tfade is severely ill posed and further apply a spectral regularization method to solve it based on the solution given by the fourier method the convergence estimate is obtained under a priori bound assumptions for the exact solution numerical examples are given to show the effectiveness of the proposed numerical method

a conservative fractional step method to solve non isentropic euler equations abstract a conservative fractional step method to solve the non isentropic euler set of equations on unstructured meshes is presented herein the present two step method which is based on approximate riemann solvers is compared with roe s scheme the actual numerical rate of convergence is examined the c f l like conditions which must be fulfilled to obtain discrete positive values of density and pressure variables are then discussed it is also shown that the extension to the multi component case enables to fulfil the maximum principle for the mass fraction

simplified tikhonov and fourier regularization methods on a general sideways parabolic equation the inverse heat conduction problem ihcp can be considered to be a sideways parabolic equation in the quarter plane and now the results available in the literature on ihcp mainly devoted to the standard sideways heat equation numerical methods have been developed also for more general equations but in most cases the stability theory and convergence proofs have not been generalized accordingly this paper remedies this by a simplified tikhonov and a new fourier regularization methods on a general sideways parabolic equation some known results for sideways heat equation are only the special case of the conclusions in this paper the numerical example shows that the computation effect is satisfactory

unicity in an inverse problem for an unknown reaction term in a reaction diffusion equation in this paper we consider an inverse problem in which we seek to deter mine an unknown source or reaction term in a reaction diffusion equation from overspecified data measured on the boundary of the spatial region where the equation applies the analysis is based on the observation that the overspecified data depends monotonically on the unknown source term in the equation here we use this monotonicity to establish a type of unicity result for the inverse problem the attractiveness of the monotonicity methods illustrated here lies in their versatility surveying the rapidly expanding literature devoted to the topic of inverse problems one finds a considerable variety of ad hoc approaches methods which apply to a general class of problems seem to be few monotonicity methods however apply to a variety of inverse problems involving partial differential equations of parabolic or elliptic type this paper is organized as follows in section 1 we formulate the direct initial boundary value problem ibvp and state assumptions on the data and a priori assumptions on the unknown source term several properties of the solution to the direct problem are derived in section 2 the principal monotonicity estimates are established and in section 3 these are applied to the inverse problem to prove a type of unicity result for the solution to the inverse problem in particular it is a corollary of theorem 3 2 that in the class of analytic source terms the solution of the inverse problem is unique the problem of identifying an unknown source term in a heat equation 155

a class of non linear non classical parabolic equations abstract in this paper we deal with a class of non classical parabolic equations which arise from some practical problems such as the identification of unknown parameters free boundary problems etc one of the characteristics of this kind of equation is that the maximum principle is no longer valid we will first study the local solvability for a general equation of this kind via an auxiliary problem and the schauder fixed point principle then some a priori estimates are derived to establish the global existence of the solution moreover uniqueness and continuous dependence of the solution are proved finally some examples are given to illustrate the applications of the theory

nonhomogeneous heat equation identification and regularization for the inhomogeneous term we study the nonhomogeneous heat equation under the form ut uxx t f x where the unknown is the pair of functions u f under various assumptions about the function and the final value in t 1 i e g x we propose different regularizations on this ill posed problem based on the fourier transform associated with a lebesgue measure for 0 the solution is unique

a multiphase godunov method for compressible multifluid and multiphase flows we propose a new model and a solution method for two phase compressible flows the model involves six equations obtained from conservation principles applied to each phase completed by a seventh equation for the evolution of the volume fraction this equation is necessary to close the overall system the model is valid for fluid mixtures as well as for pure fluids the system of partial differential equations is hyperbolic hyperbolicity is obtained because each phase is considered to be compressible two difficulties arise for the solution one of the equations is written in non conservative form non conservative terms exist in the momentum and energy equations we propose robust and accurate discretisation of these terms the method solves the same system at each mesh point with the same algorithm it allows the simulation of interface problems between pure fluids as well as multiphase mixtures several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible the method provides reliable results is able to compute strong shock waves and deals with complex equations of state

hllc type riemann solver with approximated two phase contact for the computation of the baer nunziato two fluid model abstract the computation of compressible two phase flows with the baer nunziato model is addressed only the convective part of the model that exhibits non conservative products is considered and the source terms of the model that represent the exchange between phases are neglected based on the solver proposed by tokareva toro 1 a new hllc type riemann solver is built the key idea of this new solver lies in an approximation of the two phase contact discontinuity of the model thus the riemann invariants of the wave are approximated in the subsonic case a major consequence of this approximation is that the resulting solver can deal with any equation of state it also allows to bypass the resolution of a non linear equation based on those riemann invariants we assess the solver and compare it with others on 1d riemann problems including grid convergence and efficiency studies the ability of the proposed solver to deal with complex equations of state is also investigated finally the different solvers have been compared on challenging 2d test cases due to the presence of both material interfaces and shock waves a shock bubble interaction and underwater explosions when compared with others the present solver appears to be accurate efficient and robust

optimal error bound and fourier regularization for identifying an unknown source in the heat equation in this paper we investigate a problem of the identification of an unknown source from one supplementary temperature measurement at a given instant of time for the transient heat equation under an a priori condition we answer the question concerning the best possible accuracy for the problem the fourier regularization method is utilized for solving the problem and its convergent rate is analyzed numerical results are presented to illustrate the accuracy and efficiency of the method

a modified method for a backward heat conduction problem we consider a backward heat conduction problem in a strip where data is given at the final time t t t 0 and a solution for 0 t t is sought the problem is ill posed in the sense that the solution if it exists does not depend continuously on the data in order to numerically solve the problem we study a modification of the equation where a third order mixed derivative term is added error estimates for this problem are given which show that the modified problem is stable and its solution is an approximation of the backward heat conduction problem some numerical tests illustrate that the proposed method is feasible and effective c 2006 elsevier inc all rights reserved

parallel algorithms for implicit material dynamics schemes procedures are presented for parallelizing implicit schemes for computational material dynamics these procedures are illustrated on an implicit version of the von neumann richtmyer vnr scheme the original vnr scheme a one dimensional scheme for continuum dynamics in the material reference frame has extensions to two and three dimensional and spatial reference frames the vnr codes and codes with similar structure are representative of large classes of codes accounting for large numbers of supercomputer cycles

an approximate solution for nonlinear backward parabolic equations we consider the backward parabolic equation ut au f t u t 0 t t u t g where a is a positive unbounded operator and f is a nonlinear function satisfying a lipschitz condition with an approximate datum g the problem is severely ill posed using the truncation method we propose a regularized solution which is the solution of a system of differential equations in finite dimensional subspaces according to some a priori assumptions on the regularity of the exact solution we obtain several explicit error estimates including an error estimate of holder type for all t 0 t an example on heat equations and numerical experiments are given

runge kutta discontinuous galerkin method for the approximation of baer and nunziato type multiphase models a high order numerical method is developed for the computation of compressible multiphase flows the model we use is based on the baer and nunziato type systems 4 among all the other available models in the literature these systems present the advantage to be able to simulate either interface or mixture problems nevertheless they still raise some issues mainly based on their non conservative feature the numerical method we propose is a discontinuous galerkin type in this work the interior side integrals are computed thanks to 2 robustness and high order of accuracy of the method are proved on classical interface problems but also on suitably derived analytical solutions

optimal filtering for the backward heat equation for the backward heat equation stabilized by an a priori initial bound an estimator is determined for intermediate values that is optimal with respect to the bound and the observation accuracy it is shown how this may be implemented computationally with error estimates for the computed approximation which can be made arbitrarily close to the uncertainty level induced by the ill posedness of the underlying problem thus the feasibility of this for practical computation inevitably severely limited by that inherent uncertainty is as good as possible

on the wave structure of two phase flow models we explore the relationship between two common two phase flow models usually denoted as the two fluid and drift flux models they differ in their mathematical description of momentum transfer between the phases in this paper we provide a framework in which these two model formulations are unified the drift flux model employs a mixture momentum equation and treats interphasic momentum exchange indirectly through the slip relation which gives the relative velocity between the phases as a function of the flow parameters this closure law is in general highly complex which makes it difficult to analyze the model algebraically to facilitate the analysis we express the quasi linear formulation of the drift flux model as a function of three parameters the derivatives of the slip with respect to the vector of unknown variables the wave structure of this model is investigated using a perturbation technique then we rewrite the drift flux model with a general slip relation such that it is expressed in term

a regularization parameter for nonsmooth tikhonov regularization in this paper we develop a novel rule for choosing regularization parameters in nonsmooth tikhonov functionals it is solely based on the value function and applicable to a broad range of nonsmooth models and it extends one known criterion a posteriori error estimates of the approximations are derived an efficient numerical algorithm for computing the minimizer is developed and its convergence properties are discussed numerical results for several common nonsmooth models are presented including deblurring natural images the numerical results indicate the rule can yield results comparable with those achieved with the discrepancy principle and the optimal choice and the algorithm merits a fast and steady convergence

shape from texture estimation isotropy and moments a theory is proposed for the interpretation of 3d textures with oriented elements it builds on two previous theories a statistical one due to witkin and kanatani s buffon transform we show that the statistical estimation of orientation of a textured plane is one of a general family of optimal backprojection problems which also includes maximal compactness general uniqueness and convergence results are obtained for an efficient algorithm employing second moment feedback this framework greatly enhances the usefulness of surface orientation estimation for texture in two ways first an error distribution is derived for the estimator and this is crucial for integration of shape information second hypotheses about intrinsic texture statistics can be verified by a 2 test which if failed warns that the orientation estimator is not to be believed finally it is argued that these results suggest a general moment tensor approach to analysis of 3d texture

fourier regularization for a backward heat equation abstract in this paper a simple and convenient new regularization method for solving backward heat equation fourier regularization method is given meanwhile some quite sharp error estimates between the approximate solution and exact solution are provided a numerical example also shows that the method works effectively

why many theories of shock waves are necessary kinetic relations for non conservative systems for a class of nonconservative hyperbolic systems of partial dif ferential equations endowed with a strictly convex mathematical entropy we formulate the initial value problem by supplementing the equations with a ki netic relation prescribing the rate of entropy dissipation across shock waves our condition can be regarded as a generalization to nonconservative systems of a similar concept introduced by abeyaratne knowles and truskinovsky for subsonic phase transitions and by lefloch for nonclassical undercompressive shocks to nonlinear hyperbolic systems the proposed kinetic relation for non conservative systems turns out to be equivalent for the class of systems under consideration at least to dal maso lefloch and murat s definition based on a prescribed family of lipschitz continuous paths in agreement with previous theories the kinetic relation should be derived from a phase plane analysis of traveling solutions associated with an augmented version of the nonconserva tive system we illustrate with several examples that nonconservative systems arising in the applications fit in our framework and for a typical model of turbulent fluid dynamics we provide a detailed analysis of the existence and properties of traveling waves which yields the corresponding kinetic function

model of frequency analysis in the visual cortex and the shape from texture problem this paper addresses the question at the level of cortical cells present in the primary area v1 is the information sufficient to extract the local perspective from the texture starting from a model of complex cells in visual area v1 we propose a biologically plausible algorithm for frequency analysis applied to the shape from texture problem first specific log normal filters are designed in replacement of the classical gabor filters because of their theoretical properties and of their biological plausibility these filters are separable in frequency and orientation and they better sample the image spectrum which makes them appropriate for any pattern analysis technique a method to estimate the local frequency in the image which discards the need to choose the best local scale is designed based on this frequency analysis model a local decomposition of the image into patches leads to the estimation of the local frequency variation which is used to solve the problem of recovering the shape from the texture from the analytical relation between the local frequency and the geometrical parameters under perspective projection it is possible to recover the orientation and the shape of the original image the accuracy of the method is evaluated and discussed on different kind of textures both regular and irregular with planar and curved surfaces and also on natural scenes and psychophysical stimuli it compares favorably to the best existing methods with in addition a low computational cost the biological plausibility of the model is finally discussed

shape from texture general principle abstract the 3d shape of a textured surface is recovered from its projected image on the assumption that the texture is homogeneously distributed our method does not require recognition of the structure regularity periodicity parallelism orthogonality etc of the texture distribution first the homogeneity of a discrete texture is precisely defined in terms of the theory of distributions next distortion of the observed texture due to perspective projection is described in terms of the first fundamental form expressed as a function of the image coordinates based on this result the 3d recovery equations for determining the surface shape are derived for both planar and curved surfaces some numerical schemes for solving these equations are proposed ambiguity in the interpretation of curved surfaces is also analyzed finally some numerical examples for synthetic data are presented and our method is compared with other existing methods

graph matching with a dual step em algorithm this paper describes a new approach to matching geometric structure in 2d point sets the novel feature is to unify the tasks of estimating transformation geometry and identifying point correspondence matches unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the em algorithm according to our em framework the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters these gating probabilities measure the consistency of the matched neighborhoods in the graphs the recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log likelihood function we evaluate the technique on two real world problems

numerical simulation for two phase flows using hybrid scheme the present paper is devoted to the computation of two phase flows using two fluid approach two difficulties arise for the model one of the equations is written in non conservative form non conservative terms exist in the momentum and energy equations to deal with the aforementioned difficulties the non conservative volume fraction equation is discretized by weno scheme and the cweno type central upwind scheme is applied to solve the mass momentum and energy equations computational results are eventually provided and discussed

constraint consistent runge kutta methods for one dimensional incompressible multiphase flow new time integration methods are proposed for simulating incompressible multiphase flow in pipelines described by the one dimensional two fluid model the methodology is based on halfexplicit runge kutta methods being explicit for the mass and momentum equations and implicit for the volume constraint these half explicit methods are constraint consistent i e they satisfy the hidden constraints of the two fluid model namely the volumetric flow incompressibility constraint and the poisson equation for the pressure a novel analysis shows that these hidden constraints are present in the continuous semi discrete and fully discrete equations next to constraint consistency the new methods are conservative the original mass and momentum equations are solved and the proper shock conditions are satisfied efficient the implicit constraint is rewritten into a pressure poisson equation and the time step for the explicit part is restricted by a cfl condition based on the convective wave speeds and accurate achieving high order temporal accuracy for all solution components masses velocities and pressure highorder accuracy is obtained by constructing a new third order runge kutta method that satisfies the additional order conditions arising from the presence of the constraint in combination with time dependent boundary conditions two test cases kelvin helmholtz instabilities in a pipeline and liquid sloshing in a cylindrical tank show that for time independent boundary conditions the half explicit formulation with a classic fourth order runge kutta method accurately integrates the two fluid model equations in time while preserving all constraints a third test case ramp up of gas production in a multiphase pipeline shows that our new third order method is preferred for cases featuring time dependent boundary conditions

shape from texture using local spectral moments presents a non feature based solution to the problem of computing the shape of curved surfaces from texture information first the use of local spatial frequency spectra and their moments to describe texture is discussed and motivated a new more accurate method for measuring the local spatial frequency moments of an image texture using gabor elementary functions and their derivatives is presented also described is a technique for separating shading from texture information which makes the shape from texture algorithm robust to the shading effects found in real imagery second a detailed model for the projection of local spectra and spectral moments of any surface reflectance patterns not just textures is developed third the conditions under which the projection model can be solved for the orientation of the surface at each point are explored unlike earlier non feature based curved surface shape from texture approaches the assumption that the surface texture is isotropic is not required surface texture homogeneity can be assumed instead the algorithm s ability to operate on anisotropic and nondeterministic textures and on both smooth and rough textured surfaces is demonstrated

dynamical evolution of volume fractions in multipressure multiphase flow models compared to single pressure models multipressure multiphase flow models require additional closure relations to determine the individual pressures of the different phases these relations are often taken to be evolution equations for the volume fractions we present a rigorous theoretical framework for constructing such equations for compressible multiphase mixtures in terms of submodels for the relative volumetric expansion rates ei of the phases these quantities are essentially the rates at which the phases dynamically expand or contract in response to pressure differences and represent the general tendency of the volume fractions to relax toward values that produce local pressure equilibrium we present a simple provisional model of this type in which ei is proportional to pressure differences divided by the time required for sound waves to traverse an appropriate characteristic length it is shown that the resulting approach to pressure equilibrium is monotonic rather than oscillatory and occurs instantaneously in the incompressible limit

hyperbolic two pressure models for two phase flow revisited this paper presents correction to a previous paper j comput phys 53 1984 124 on stability analyses of one pressure models for two phase flow it also presents some extensions and generalization of previous work on two pressure models the extensions allow both the slopes to the interfaces and the rates of mass transfer through the interfaces to be non negligible these enlargements of the domain of applicability of the two pressure models introduce extra derivative terms into the models these extra derivative terms do not change the basic character of the model the two pressure models remain stable in the sense of von neumann a e in state space with the more complete modeling of the interface copyright 1988 academic press inc

estimation of orientation of a textured planar surface using projective equations and separable analysis with m channel wavelet decomposition estimation of the orientation of a textured planar surface is one of the basic tasks in the area of shape from texture for the solution of this task many successful approaches were proposed in this paper we have examined a few unaddressed questions first is there a mathematical formulation that relates the spectral characteristics of the texture pattern and the orientation of an inclined planar surface in a polar coordinate system second is there a good wavelet based approach that produces an accurate estimate of the orientation angle of the textured planar surface by analyzing the spectral behavior of one single uncalibrated image to answer these questions at first we present the formulation of a texture projective equation which relates the depth and orientation of an inclined planar surface in a polar coordinate system with the spectral properties of its image texture a suitable imaging geometry has been considered to enable separable analysis of the effect of inclination of the texture surface next a method for shape from texture is presented based on discrete wavelet analysis to estimate the orientation of the planar surface this approach although designed mainly for m channel wavelets is also applicable for dyadic wavelet analysis texture characteristics in the subbands of wavelet decomposition are analyzed using scalograms and quantitatively evaluated based on texture projective equations the proposed method of estimation of the orientation of a planar texture surface is evaluated using a set of simulated and real world textured images

nonlinear generalized functions and jump conditions for a standard one pressure liquid gas model abstract the mixture of a liquid and a gas is classically represented by one pressure models these models are a system of pdes in nonconservative form and shock wave solutions do not make sense within the theory of distributions they give rise to products of distributions that are not defined within distribution theory but they make sense by applying a theory of nonlinear generalized functions to these equations in contrast to the familiar case of conservative systems the jump conditions cannot be calculated a priori jump conditions for these nonconservative systems can be obtained using the theory of nonlinear generalized functions by inserting some adequate physical information into the equations the physical information that we propose to insert for the one pressure models of a mixture of a liquid and a gas is a natural mathematical expression in the theory of nonlinear generalized functions of the fact that liquids are practically incompressible while gases are very compressible and so they do not satisfy equally well their respective state laws on the shock waves this modelization gives well defined explicit jump conditions the great numerical difficulty for solving numerically nonconservative systems is due to the fact that slightly different numerical schemes can give significantly different results the jump conditions obtained above permit to select the numerical schemes and validate those that give numerical solutions that satisfy these jump conditions which can be an important piece of information in the absence of other explicit discontinuous solutions and of precise observational results we expose with care the mathematical originality of the theory of nonlinear generalized functions an original abstract analysis issued by the leopoldo nachbin team on infinite dimensional holomorphy that permits to state mathematically physical facts that cannot be formulated within distribution theory and are the key for the removal of ambiguities that classically appear when one tries to calculate on multiplications of distributions that occur in the differential equations of physics

an approximate linearized riemann solver for a two fluid model an approximate linearized riemann solver is presented for the numerical simulation of two phase flows this new solver is based on a linearization of nonconservative products and uses an extension of roe s approximate riemann solver the scheme is applied to shock tube problem and to a standard test for two fluid codes

numerical solution of forward and backward problem for 2 d heat conduction equation for a two dimensional heat conduction problem we consider its initial boundary value problem and the related inverse problem of determining the initial temperature distribution from transient temperature measurements the conditional stability for this inverse problem and the error analysis for the tikhonov regularization are presented an implicit inversion method which is based on the regularization technique and the successive over relaxation sor iteration process is established due to the explicit difference scheme for a direct heat problem developed in this paper the inversion process is very efficient while the application of sor technique makes our inversion convergent rapidly numerical results illustrating our method are also given

existence and uniqueness properties for the one dimensional magnetotellurics inversion problem the one dimensional magnetotelluric mt inversion problem is well known to be ill posed and nonlinear this paper seeks an understanding of the mappings underlying the nonlinear relationships these properties are used to study the validity of some exploration aspects of the problem that are essential for the practical use of mt as an exploration tool this study has two major segments results in response space and results in geologic space in response space the existence of optimal admittance curves has been proven in the case of continuous data uniqueness has been established for discrete data a relationship between alternative optimal solutions has been derived in geologic space the results are extremely significant to mt s applicability to exploration a class of conductivity functions y which contains all possible natural geological conditions has been used as a framework for the study over this class y the one dimensional magnetotellurics problem has been proven to be uniquely invertible from the admittance curves this precludes the possibility of two different geologic models yielding the same complete data as a result the path is now clear to generate a description of a unimodal statistical distribution of feasible inversions to the real world exploration problem with finitely sampled noisy data

a comparison of regularizations for an ill posed problem we consider numerical methods for a quasi boundary value regularization of the backward parabolic problem given by u t au 0 0 t t u t f where a is positive self adjoint and unbounded the regularization due to clark and oppenheimer perturbs the final value u t by adding u 0 where is a small parameter we show how this leads very naturally to a reformulation of the problem as a second kind fredholm integral equation which can be very easily approximated using methods previously developed by ames and epperson error estimates and examples are provided we also compare the regularization used here with that from ames and epperson

central finite volume schemes on nonuniform grids and applications we propose a new one dimensional unstaggered central scheme on nonuniform grids for the numerical solution of homogeneous hyperbolic systems of conservation laws with applications in two phase flows and in hydrodynamics with and without gravitational effect the numerical base scheme is a generalization of the original lax friedrichs scheme and an extension of the nessyahu and tadmor central scheme to the case of nonuniform irregular grids the main feature that characterizes the proposed scheme is its simplicity and versatility in fact the developed scheme evolves a piecewise linear numerical solution defined at the cell centers of a nonuniform grid and avoids the resolution of the riemann problems arising at the cell interfaces thanks to a layer of staggered cells used intermediately spurious oscillations are avoided using a slopes limiting procedure the developed scheme is then validated and used to solve classical problems arising in gas solid two phase flow problems the proposed scheme is then extended to the case of non homogenous hyperbolic systems with a source term in particular to the case of euler equations with a gravitational source term the obtained numerical results are in perfect agreement with corresponding ones appearing in the recent literature thus confirming the efficiency and potential of the proposed method to handle both homogeneous and non homogeneous hyperbolic systems

an efficient high order algorithm for solving systems of 3 d reaction diffusion equations we discuss an efficient higher order finite difference algorithm for solving systems of 3 d reaction diffusion equations with nonlinear reaction terms the algorithm is fourth order accurate in both the temporal and spatial dimensions it requires only a regular seven point difference stencil similar to that used in the standard second order algorithms such as the crank nicolson algorithm numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm

shape from regular patterns niis paper describes an aigoritlitr1 to obtaitl local surface orierltatiorr frofti the apparetlt surface pattertl distortion in an image we propose a spherical projection to model perspctiue imaging a trtappitlg is debtled based of1 the measurement of the local distortions of a repeated known rexture pattern due io the image projection 77tis mapping maps an apparent shape on the image sphere lo a locus of possible surface orienrations on the gaussian sphere an ireratiw constraint propagation algorithm with the orientations at occluding boundaries reduces possible surface orientations to a unique orientation 7lis algorithm can recover local surface orientation as well as interpolate surjace orientations where no information is auailable xis algorithm is applied to a real image ro demonstrate its perfontlance

macroscopic theory of multicomponent flows irreversibility and well posed equations abstract a theory of the coupling of n systems of navier stokes equations is presented a set of coupled navier stokes systems contains the macroscopic equations of motion for flows of n different material components or phases six postulates are formulated from which three navier stokes sets are derived for arbitrary n the main postulate concerns the second law of thermodynamics which the present sets satisfy for arbitrary n appropriate averages of velocities and pressures distribute the entropy production of each irreversible interaction process among the interacting components increase of entropy is guaranteed if the interaction terms are suitably constructed from positive definite operators a strictly irreversible mass exchange law expressed in the difference of gibbs free energies of the exchanging components is proposed furthermore the characteristic velocities of each navier stokes set are investigated since their realness is required for well posedness of the equations for both navier stokes sets with multiple pressures the characteristic velocities are proven to be real for arbitrary n the canonical problem of complex characteristics of incompressible multiphase flows with a single pressure is revisited a solution to this problem is found by generalizing the standard algebraic stokes drag law to a positive definite operator acting on the velocity difference in this way effects of forces due to nonuniform velocity fields can be incorporated a generalized drag law is specified by the inclusion of m th order spatial derivatives of the velocity differences between two components m 2 the characteristic polynomial is derived for an arbitrary number of components and its roots the characteristic velocities appear to be real this is rigorously proven for two and three phase flows and conjectured to be true for flows with four or more components the linear stability of the incompressible one dimensional case is also investigated ill posedness of the standard case leads to an infinite growth rate for infinitely short waves in the case of generalized drag this growth rate becomes finite for even and neutral for odd m

solving the inverse problem of identifying an unknown source term in a parabolic equation the inverse problem of determining an unknown source term in a parabolic equation with the leading coefficient depending on time and space variables under a final overdetermination condition is considered the series pattern solution of the problem is obtained by using the weighted homotopy analysis method wham a description of the method for solving the problem and identifying the unknown source term is derived finally several examples are presented to illustrate this method

planar surface orientation from texture spatial frequencies abstract this paper presents a computational model and a practical algorithm for determining the three dimensional orientation of a planar surface from visual texture information the model consists of three parts 1 a local spatial frequency based texture representation 2 a model describing the projection of surface texture to image texture and 3 a solution of the texture projection model for the surface orientation under an assumption of surface texture homogeneity the algorithm first measures the dominant frequency at each image point using three wavelet like transforms and then finds the surface orientation that minimizes the variance of the image frequencies backprojections the algorithm is tested on photographs of real world surfaces exhibiting an average accuracy of better than 3 in slant and 4 in tilt the current model and algorithm are more accurate yet substantially simpler than earlier versions of this approach

numerical simulation of a compressible two layer model a first attempt with an implicit explicit splitting scheme this work is devoted to the numerical simulation of the compressible two layer model developed in 16 the latter is an hyperbolic two fluid two pressure model dedicated to gas liquid flows in pipes especially stratified air water flows using explicit schemes one obtains a cfl condition based on the celerity of fast acoustic waves which typically brings large numerical diffusivity for the slow material waves and small time steps in order to overcome these drawbacks the proposed scheme involves an operator splitting and an implicit explicit time discretization thus the full system is split into two hyperbolic subsystems the first one deals with the transport equation on the liquid height using an explicit scheme and upwind fluxes the second one deals with the averaged mass and momentum conservation equations of both phases using an implicit scheme which handles the propagation of acoustic waves at last the positivity of heights and densities is ensured under a cfl condition which involves material velocities numerical experiments are performed using acoustic as well as material time steps adding the rusanov scheme for comparison the best accuracy is obtained with the proposed scheme used with acoustic time steps when used with material time steps efficiency on the slow waves and stability are obtained regarding analytical solutions of the convective part

source term identification in 1 d ihcp we propose stable numerical solutions for the simultaneous identification of temperature temperature gradient and general source terms in the one dimensional inverse heat conduction problem ihcp the numerical solution consists of a regularization procedure based on the mollification method and a marching scheme for the solution of the stabilized problem the stability error analysis and implementation of the algorithm are presented together with a set of numerical results

the boundary element method for the solution of the backward heat conduction equation in this paper we consider the numerical solution of the one dimensional unsteady heat conduction equation in which dirichlet boundary conditions are specified at two space locations and the temperature distribution at a particular time say t0 is given the temperature distribution for all times t t0 is now required and this backward heat conduction problem is a well known improperly posed problem in order to solve this problem the minimal energy technique has been introduced in order to modify the boundary element method and this results in a stable approximation to the solution and the accuracy of the numerical results are very encouraging

hybrid flux splitting schemes for a two phase flow model in this paper we deal with the construction of hybrid flux vector splitting fvs schemes and flux difference splitting fds schemes for a two phase model for one dimensional flow the model consists of two mass conservation equations one for each phase and a common momentum equation the complexity of this model as far as numerical computation is concerned is related to the fact that the flux cannot be expressed in terms of its conservative variables this is the motivation for studying numerical schemes which are not based on approximate riemann solvers and or calculations of jacobian matrix this work concerns the extension of an fvs type scheme a van leer type scheme and an advection upstream splitting method ausm type scheme to the current two phase model our schemes are obtained through natural extensions of corresponding schemes studied by y wada and m s liou 1997 siam j sci comput 18 633 657 for euler equations we explore the various schemes for flow cases which involve both fast and slow transients in particular we demonstrate that the fvs scheme is able to capture fast propagating acoustic waves in a monotone way while it introduces an excessive numerical dissipation at volume fraction contact steady and moving discontinuities on the other hand the ausm scheme gives accurate resolution of contact discontinuities but produces oscillatory approximations of acoustic waves this motivates us to propose other hybrid fvs fds schemes obtained by removing numerical dissipation at contact discontinuities in the fvs and van leer schemes

shape from periodic texture using the eigenvectors of local affine distortion shows how the local slant and tilt angles of regularly textured curved surfaces can be estimated directly without the need for iterative numerical optimization we work in the frequency domain and measure texture distortion using the affine distortion of the pattern of spectral peaks the key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles of tangent planes to curved surfaces in particular the leading eigenvector points in the tilt direction although not as geometrically transparent the direction of the second eigenvector can be used to estimate the slant direction the required affine distortion matrices are computed using the correspondences between spectral peaks established on the basis of their energy ordering we apply the method to a variety of real world and synthetic imagery

obtaining a 3 d orientation of projective textures using a morphological method on the premise that the texture image is a planar surface we propose a new morphological approach to obtain a 3 d surface orientation using the variation of texture image caused by projective distortions centroids of texels can be obtained from the farthest texel to the nearest texel sequentially by recursive erosions so a texture image is segmented into several sub regions using major axes and sizes of structuring elements in segmented regions we can compute a vanishing point and obtain a 3 d surface orientation in the experiments we have ascertained the proposed algorithm was more effective than the aggregation transform

numerical resolution for a compressible two phase flow model based on the theory of thermodynamically compatible systems this paper is concerned with the numerical solution of the equations governing two phase gas solid mixture in the framework of thermodynamically compatible systems theory the equations constitute a non homogeneous system of nonlinear hyperbolic conservation laws a total variation diminishing tvd slope limiter centre slic numerical scheme based on the splitting approach is presented and applied for the solution of the initial boundary value problem for the equations the model equations and the numerical methods are systematically assessed through a series of numerical test cases strong numerical evidence shows that the model and the methods are accurate robust and conservative the model correctly describes the formations of shocks and rarefactions in two phase gas solid flow

source term identification for an axisymmetric inverse heat conduction problem we consider an inverse heat source problem of determining the heat source term from the final temperature history of a cylinder this problem is ill posed a simplified tikhonov regularization method is applied to formulate regularized solution which is stably convergent to the exact one with a logarithmic type error estimate

hyperbolic two pressure models for two phase flow abstract for some time it has been known that many of the two phase flow models lead to ill posed cauchy problems because they have complex characteristic values a necessary condition at least in the linear case for the cauchy problem to be well posed is that it be stable in the sense of von neumann for systems of partial differential equations of first order stability in the sense of von neumann is essentially equivalent to the condition that the model be hyperbolic all real characteristic values and complete set of characteristic vectors herein models are developed which have real characteristic values for all physically acceptable states state space and except for a set of measure zero have a complete set of characteristic vectors in state space therefore these models are hyperbolic a e almost everywhere in state space also they are stable in the sense of von neumann a e in state space even without inclusion of viscosity terms the models discussed herein are developed for the case of two phase separated planar flow and include transverse momentum considerations these models are referred to as two pressure models because each phase is assumed to exist at an average pressure different from the average pressure in the other phase the pressure fields are related through momentum considerations numerical results on a steady state problem show good agreement with existing steady state results numerical results on a transient problem agree with a single pressure model until the onset of numerical instability in the single pressure model compared to the single pressure hydrostatic model the two pressure model approximates additional physical features and is shown to be a viable approach for the case of separated flow

new constraints on data closeness and needle map consistency for shape from shading this paper makes two contributions to the problem of needle map recovery using shape from shading first we provide a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint this not only improves the data closeness of the recovered needle map but also removes the necessity for extensive parameter tuning second we exploit the improved ease of control of the new shape from shading process to investigate various types of needle map consistency constraint the first set of constraints are based on needle map smoothness the second avenue of investigation is to use curvature information to impose topographic constraints third we explore ways in which the needle map is recovered so as to be consistent with the image gradient field in each case we explore a variety of robust error measures and consistency weighting schemes that can be used to impose the desired constraints on the recovered needle map we provide an experimental assessment of the new shape from shading framework on both real world images and synthetic images with known ground truth surface normals the main conclusion drawn from our analysis is that the data closeness constraint improves the efficiency of shape from shading and that both the topographic and gradient consistency constraints improve the fidelity of the recovered needle map

a five equation reduced model for compressible two phase flow problems this paper studies an eulerian diffuse interface model for the simulation of compressible multifluid and two phase flow problems we first show how to derive this model from a seven equation two pressure two velocity model of baer nunziato type using an asymptotic analysis in the limit of zero relaxation time we then study the mathematical properties of the system the structure of the waves the expression of the riemann s invariants and the existence of a mathematical entropy we also describe two different numerical approximation schemes for this system the first one relies on a linearized riemann solver while the second uses more heavily the mathematical structure of the system and relies on a linearization of the characteristic relations finally we present some numerical experiments and comparisons with the results obtained by the two pressure two velocity model as well as some test cases and comparisons with another five equation model recently proposed for interface computations between compressible fluids

an a posteriori parameter choice rule for the truncation regularization method for solving backward parabolic problems the goal of this paper is to investigate a backward parabolic equation with time dependent coefficient by the truncation method tm the key point to our paper is that we give an a posteriori choice of regularization parameter for the tm with which the convergence estimates between the exact solution and the regularized approximation are obtained numerical implementation sheds light on the accuracy and efficiency of the proposed method

surface orientation from projective foreshortening of isotropic texture autocorrelation a method for determining local surface orientation from the autocorrelation function of statistically isotropic textures is introduced it relies on the foreshortening that occurs in the image of an oriented surface and the analogous foreshortening produced in the texture autocorrelation function this method assumes textural isotropy but does not require the texture to be composed of texels or assume other texture regularities the technique was applied to natural images of planar textured surfaces and found to give good results the simplicity of the method and its use of information from all parts of the image are emphasized

a nearly implicit hydrodynamic numerical scheme for two phase flows this article presents an extension of the semi implicit numerical scheme for two phase flow simulation the extension uses an implicit evaluation of the convective fluxes and thus eliminates the material courant stability restriction the new algorithm involves a two step approach for the mass and energy equations and a single fully implicit step for the momentum evaluations some analysis and accuracy considerations for the scheme are also presented

discontinuous galerkin finite element methods for hyperbolic nonconservative partial differential equations we present space and space time discontinuous galerkin finite element dgfem formulations for systems containing nonconservative products such as occur in dispersed multiphase flow equations the main criterium we pose on the weak formulation is that if the system of nonconservative partial differential equations can be transformed into conservative form then the formulation must reduce to that for conservative systems standard dgfem formulations cannot be applied to nonconservative systems of partial differential equations we therefore introduce the theory of weak solutions for nonconservative products into the dgfem formulation leading to the new question how to define the path connecting left and right states across a discontinuity the effect of different paths on the numerical solution is investigated and found to be small we also introduce a new numerical flux that is able to deal with nonconservative products our scheme is applied to two different systems of partial differential equations first we consider the shallow water equations where topography leads to nonconservative products in which the known possibly discontinuous topography is formally taken as an unknown in the system second we consider a simplification of a depth averaged two phase flow model which contains more intrinsic nonconservative products

a numerical technique for backward inverse heat conduction problems in one dimensional space in this article we consider an inverse heat conduction problem in one dimensional space with two unknown terms in this problem the initial temperature and histories of temperature in the finite interval of time may be determined then by using a semi implicit finite difference method an estimation of these unknown terms will be found obviously this problem is ill posed but by applying a suitable parameter we can obtain the best of these estimations finally some numerical experiments are given in the final section of this paper

weakly implicit numerical schemes for a two fluid model the aim of this paper is to construct semi implicit numerical schemes for a two phase two fluid flow model allowing for violation of the cfl criterion for sonic waves while maintaining a high level of accuracy and stability on volume fraction waves by using an appropriate hybridization of a robust implicit flux and an upwind explicit flux we obtain a class of first order schemes which we refer to as weakly implicit mixture flux wimf methods in particular by using an advection upstream splitting method ausmd type of upwind flux s evje and t flatten j comput phys 192 2003 pp 175 210 we obtain a scheme denoted as wimf ausmd we present several numerical simulations all of them indicating that the cfl stability of the wimf ausmd scheme is governed by the velocity of the volume fraction waves and not the rapid sonic waves comparisons with an explicit roe scheme indicate that the scheme presented in this paper is highly efficient robust and accurate on slow transients by exploiting the possibility to take much larger time steps it outperforms the roe scheme in the resolution of the volume fraction wave for the classical water faucet problem on the other hand it is more diffusive on pressure waves although conservation of positivity for the masses is not proved we demonstrate that a fix may be applied making the scheme able to handle the transition to one phase flow while maintaining a high level of accuracy on volume fraction fronts

a non local boundary value problem method for parabolic equations backward in time abstract the ill posed parabolic equation backward in time u t a u 0 0 t t u t f subject to the constraint u 0 e with the positive self adjoint unbounded operator a and e 0 being given is regularized by the well posed non local boundary value problem u t a u 0 0 t t u 0 u t f 0 the error estimates of holder type of the regularized solutions are obtained these estimates improve the related results by mel nikova denche and bessila

a backward parabolic equation with a time dependent coefficient regularization and error estimates we consider the problem of determining the temperature u x t for x t 0 p x 0 t in the parabolic equation with a time dependent coefficient this problem is severely ill posed i e the solution if it exists does not depend continuously on the given data in this paper we use a modified method for regularizing the problem and derive an optimal stability estimation a numerical experiment is presented for illustrating the estimate

asymptotic study of the initial value problem to a standard one pressure model of multifluid flows in nondivergence form abstract we construct families of approximate solutions to the initial value problem and provide complete mathematical proofs that they tend to satisfy the standard system of isothermal one pressure two fluid flows in 1 d when the data are l 1 in densities and l in velocities to this end we use a method that reduces this system of pdes to a family of systems of four odes in banach spaces whose smooth solutions are these approximate solutions this method is constructive using standard numerical methods for odes one can easily and accurately compute these approximate solutions which therefore from the mathematical proof can serve for comparison with numerical schemes one observes agreement with previously known solutions from scientific computing evje and flatten 2003 16 we show that one recovers the solutions of these authors exactly in one case with a slight difference in another case then we propose an efficient numerical scheme for the original system of two fluid flows and show it gives back exactly the same results as the theoretical solutions obtained above

heuristic parameter choice rules for convex variational regularization based on error estimates in this paper we are interested in heuristic parameter choice rules for general convex variational regularization which are based on error estimates two such rules are derived and generalize those from quadratic regularization namely the hanke raus rule and quasi optimality criterion a posteriori error estimates are shown for the hanke raus rule and convergence for both rules is also discussed numerical results for both rules are presented to illustrate their applicability

control parameter estimation in a semi linear parabolic inverse problem using a high accurate method abstract parabolic inverse problems have an important role in many branches of science and technology the aim of this research work is to solve these classes of equations using a high order compact finite difference scheme we consider the following inverse problem for finding u x t and p t governed by u t u xx p t u x t with an over specified condition inside the domain spatial derivatives are approximated using central difference scheme the time advancement of the simulation is performed using a third order compact runge kutta method the convergence orders for the approximation of both u and p are of o k 3 h 2 which improves the results obtained in the literature an exact test case is used to evaluate the validity of our numerical analysis we found that the accuracy of the results is better than that of previous works in the literature

a musta scheme for a nonconservative two fluid model we present a multistage centered scheme of the kind proposed by toro appl numer math 56 2006 pp 1464 1479 for numerically resolving the simultaneous flow of two fluids through a transport pipeline this model contains nonconservative terms in both the temporal and spatial derivatives and an extension of the standard numerical framework for conservation laws is needed in this paper we rewrite the model in an equivalent mathematical form eliminating the nonconservative time derivatives this allows us to use the framework described by pares siam j numer anal 44 2006 pp 300 321 we develop force and musta type schemes which are consistent with pares formalism numerical simulations demonstrate a high degree of stability of our proposed schemes comparisons with the roe and rusanov schemes indicate that convergence to near identical solutions is obtained when the nonconservative terms are discretized with respect to the same evaluation of the path dependent integrals however if the schemes are not mutually formally path consistent in the sense of pares different converged solutions are obtained

identification of source terms in 2 d ihcp abstract we introduce a stable numerical space marching scheme based on discrete mollification implemented as an automatic adaptive filter for the approximate identification of temperature temperature gradient and source terms in the two dimensional inverse heat conduction problem ihcp the stability and error analysis of the algorithm together with some numerical examples are provided

determination of a term in the right hand side of parabolic equations the inverse problem of determining a term in the right hand side of parabolic equations from integral observations is investigated the observations can be regarded as generalized interior point observations which are collected in practice the problem is then reformulated as a least squares problem in coupling with a tikhonov regularization term it is proved that the tikhonov functional is frechet differentiable and a formula for the gradient is derived via an adjoint problem the variational problem is discretized by the finite element method the convergence of which is proved the discretized variational problem is numerically solved by the conjugate gradient method some numerical examples are presented for showing the efficiency of the method

traveling waves solution of convection diffusion systems whose convection terms are weakly nonconservative application to the modeling of two phase fluid flows the paper is concerned with the derivation of explicit approximate jump conditions for the shock waves solutions of hyperbolic systems in nonconservation form extracted from a known second order convection diffusion system the shock waves are defined as the limit as the diffusion tends to zero of the traveling waves solution of the second order system although no explicit jump conditions may be found for general hyperbolic systems in nonconservation form we derive an asymptotic expansion of the nonexplicit jump relations in the case of two phase fluid flows we indeed observe that the terms in nonconservation form arise from pressure gradient forces which act on droplets and are small in the sense that the a small number appears in front of them we obtain an asymptotic expansion of the nonexplicit jump relations whose first two terms can be computed explicitly

entropy and tikhonov based regularization techniques applied to the backwards heat equation abstract the goal of this paper is to analyze the performance of different regularization techniques for an inverse heat conduction problem ihcp the estimation of the initial condition the inverse problem is formulated as a nonlinear constrained optimization problem and a regularization term is added to the objective function with the help of a regularization parameter three classes of regularization methods have been considered tikhonov regularization maximum entropy principle and truncated singular value decomposition concerning the entropic methodology two new techniques are introduced and good results were obtained using synthetic data corrupted with noise the morozov s discrepancy principle is used to find out the regularization parameter

the fractional tikhonov regularization methods for identifying the initial value problem for a time fractional diffusion equation abstract in this paper we identify the initial value for a time fractional diffusion equation on a columnar axis symmetric domain this problem is ill posed i e the solution if it exists does not depend continuously on the domain two different kinds of fractional tikhonov methods are used to solve this problem under the a priori and the a posteriori regularization parameter choice rules the error estimates between the regularization solutions and the exact solution are obtained respectively different numerical examples are presented to illustrate the validity and effectiveness of our methods

finite volume algorithm to compute dense compressible gas solid flows a finite volume scheme is presented that allows the performance of numerical simulations of a four equation compressible two fluid model on unstructured meshes the convective part of the whole set of governing equations is a nonconservative conditionally hyperbolic system to solve the latter a fractional step method is presented which is based on a splitting of convective fluxes approximate roe type riemann solvers are used to compute numerical convective fluxes some computations of shock tube test cases are presented and compared with numerical results of a three equation model which assumes equal velocities within each phase a steady computation of a gas solid flow in a simple nozzle is described and an unsteady computation of a dense fluidized bed is also presented particular emphasis is given to the preservation of the maximum principle for the volumetric fraction

fractional step methods for thermohydraulic calculation abstract a method of fractional steps is used to extend a semi implicit finite difference technique for multidimensional two phase flow calculations this extension permits time step size to be chosen independent of convection velocities in one space direction and still resolves multidimensional coupled sonic and phase exchange effects implicitly by forming a simple poisson problem for pressure because pure time splitting by physical phenomena was found unsuited to thermal hydraulics problems a stabilizing corrections method was chosen an application in nuclear reactor safety analysis is demonstrated

detection of time varying heat sources using an analytic forward model abstract we present a simple analytic point source model for both static and time varying point like heat sources and the resulting temperature profile that solves the heat equation in dimension three simple algorithms to detect the location and spectral content of these sources are developed and numerically tested using finite element mesh simulations the resulting framework for heat source reconstruction problems which are ill posed inverse problems seems promising and warrants for future research possible fields of application for our work are material testing to detect manufacturing defects and medical imaging to detect abnormal health conditions

numerical solutions of one pressure models in multifluid flows flows of a mixture of several fluids can be described by one pressure models their formulation is formally simple and their efficiency has been recognized but from the mathematical viewpoint they present severe peculiarities they are not hyperbolic appear to be ill posed and are in nonconservative form so they show ambiguous products of distributions in case of shock waves a resolution of these ambiguities is proposed it gives jump conditions similar to the classical rankine hugoniot jump conditions of conservative systems this resolution attempts to solve the riemann problem and then the cauchy problem by godunov type schemes following nonconservative techniques initiated by a y le roux and collaborators

eigenform error estimates of computational material dynamics with shocks 1 1 hooke s law materials abstract eigenform error estimates are sharper than previous a priori error bounds for the von neumann richtmyer vnr scheme theoretical results give insight into the experimental results on the test problems which include shocks the vnr rk4 scheme a runge kutta modification of the original vnr is not only more accurate than the original vnr but also the eigenform error estimates are more accurate for vnr rk4