an implicit finite volume method for the solution of 3d low mach number viscous flows using a local preconditioning technique this paper presents a cell centered high order finite volume scheme for the solution of the three dimensional 3d navier stokes equations with low mach number the system of non linear equations is solved by means of a fully implicit pseudo transient scheme each pseudo time step is solved by a newton gmres procedure a local preconditioning technique is used to scale the speed of sound and to improve the system condition number for low mach number and low cell reynolds number this preconditioning is applied to the ausm up flux vector splitting function the method is tested on 2d and 3d low mach number laminar flows

zero temperature error correcting code for a binary symmetric channel we study a convolutional error correcting code with a minimum error probability decoding procedure which is designed to lower the distortion of messages transmitted through a noisy binary symmetric channel the problem can be rephrased in terms of zero temperature properties of a one dimensional disordered spin model with random two and three spin couplings for instance the ground state magnetization is related to the average error per bit of decoded output messages the ground state energy is evaluated exactly whereas other relevant quantities are expanded as power series in the density p of impurity couplings a measure of the level of channel noise these analytic results are compared with the outcomes of numerical simulations

efficient computational model for inductive plasma flows a new approach to the numerical modeling of inductive plasmas is presented the governing magnetohydrodynamic equations are discretized in a second order accurate finite volume manner a straightforward pressure stabilized flow field solver is introduced as an alternative to the staggered mesh solvers used in traditional algorithms it is argued that the widely used integral boundary formulation for the electric field is computationally expensive and cannot be incorporated into an efficient iterative solution procedure this approach is abandoned in favor of a far field formulation of the electric field such that powerful iterative methods can be applied to speed up the calculation the discretized equations are solved through a damped picard method and an approximate and full newton method efficient linear algebra methods are used to solve the linear systems arising from the iterative methods an appropriate linearization of the strongly positive joule heating source term is important for the convergence at the linear level the new model is tested on an lte argon inductive plasma computation the proposed approximate newton method is found to converge substantially better than the picard method the full newton method appears promising although its successful use on fine meshes still requires improvements to the linear solver used

analysis of mathematical models for the growth of tumors with time delays in cell proliferation we study two mathematical models for the growth of tumors with time delays in cell proliferation one for nonnecrotic tumors in the presence of inhibitors and the other for necrotic tumors mathematical formulations of these models are retarded differential equations by using a comparison method we make rigorous analysis of these models the results show that dynamical behavior of solutions of these models are similar to that of solutions for corresponding nonretarded problems and the tumor will tend to a dormant state as time goes to infinity in favorable conditions nutrient sufficient inhibitor less while it will finally disappear in unfavorable conditions nutrient insufficient inhibitor much

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

an improved unsteady unstructured artificial compressibility finite volume scheme for viscous incompressible flows part i theory and implementation a robust artificial compressibility scheme has been developed for modelling laminar steady state and transient incompressible flows over a wide range of reynolds and rayleigh numbers artificial compressibility is applied in a consistant manner resulting in a system of preconditioned governing equations a locally generalized preconditioner is introduced designed to be robust and offer good convergence rates free artificial compressibility parameters in the equations are automated to allow ease of use while facilitating improved or comparable convergence rates as compared with the standard artificial compressibility scheme memory efficiency is achieved through a multistage pseudo time explicit time marching solution procedure a node centred dual cell edge based finite volume discretization technique suitable for unstructured grids is used due to its computational efficiency and high resolution spatial accuracy in the interest of computational efficiency and ease of implementation stabilization is achieved via a scalar valued artificial dissipation scheme temporal accuracy is facilitated by employing a second order accurate dual time stepping method in this part of the paper the theory and implementation details are discussed in part 11 the scheme will be applied to a number of example problems to solve flows over a wide range of reynolds and rayleigh numbers

a numerical analysis of a model of growth tumor in this paper we study a free boundary problem modeling the growth of tumors the model uses the conventional ideas of nutrient diffusion and consumption by the cells we consider the radially symmetric case of this free boundary problem we apply a spectral numerical method to the system of equations

the application of preconditioning in viscous flows a time derivative preconditioning algorithm that is effective over a wide range of flow conditions from inviscid to very diffusive flows and from low speed to supersonic flows has been developed the algorithm uses a preconditioning matrix that introduces well conditioned eigenvalues while simultaneously avoiding nonphysical time reversals for viscous flows the resulting algorithm also provides a mechanism for controlling the inviscid and viscous time step parameters at very diffusive flows thereby ensuring rapid convergence for very viscous flows as well as for inviscid flows computational capabilities are demonstrated through computation of a wide variety of problems convergence rates are shown to be accelerated by as much as two orders of magnitudes while providing solutions that are indentical to those obtained without preconditioning method

blended ausm method for all speeds and all grid aspect ratios an ausm based discretization method using an explicit third order discretization for the convective part and a line implicit central discretization for the acoustic part and for the diffusive part has been developed for incompressible and low speed compressible navier stokes equations the lines are chosen in the direction of the gridpoints with shortest connection the semi implicit line method is used in multistage form because of the explicit third order discretization of the convective part multigrid is used as acceleration technique because of the implicit treatment of the acoustic and the diffusive terms the stiffness otherwise caused by high aspect ratio cells is removed low mach number stiffness is treated by a preconditioning technique to ensure physical correct behavior of the discretization for vanishing mach number extreme care has been taken for vanishing mach number stabilization terms are added to the mass flux pressure and temperature stabilization terms are necessary the coefficients of these terms are chosen so that correct scaling with mach number is obtained a blend of the low speed algorithm with the original ausm algorithm developed for high speed applications has been constructed so that the resulting algorithm can be used at all speeds

preconditioned hlle method for flows at all mach numbers a two dimensional preconditioned multigrid navier stokes solver has been developed for all mach number viscous flows for the computation of all mach number flows a local preconditioning technique with a modified reference velocity was used to extend the harten lax van leer einfeldt hlle scheme which has good characteristics for compressible viscous flows the developed methods used to compute several representative steady problems grid refinement and parametric studies are performed to verify the performance the results show that the preconditioned hlle scheme can be successfully applied to a wide variety of flows and that the implicit multigrid solver provides good convergence for the test problems

a unified finite element formulation for compressible and incompressible flows using augmented conservation variables abstract a unified approach to computing compressible and incompressible flows is proposed the governing equation for pressure is selected based on the local mach number in the incompressible limit the divergence free constraint on velocity field determines the pressure while it is the equation of state that governs the pressure solution for the compressible flows stabilized finite element formulations based on the space time and semi discrete methods with the augmented conservation variables are employed the augmented conservation variables consist of the usual conservation variables and pressure as an additional variable the formulation is applied to various test problems involving steady and unsteady flows over a large range of mach and reynolds numbers

a low dissipation dg method for the under resolved simulation of low mach number turbulent flows abstract in recent years the use of high order discontinuous galerkin dg methods for the under resolved direct numerical simulations udns of turbulent flows has received special attention the suitability of the approach for this kind of applications is related to the dissipation and dispersion proprieties of the scheme while the dispersion errors are small over a broad range of frequencies a relevant dissipation error mainly acts at the smallest under resolved scales resembling a high frequency filter nevertheless it was recognized flad and gassner 2017 mengaldo et al 2018 that the choice of the interface convective numerical flux strongly affects this dissipation behaviour and ultimately the success of the udns approach in this regard the excess of numerical dissipation caused by some upwind numerical convective fluxes must be avoided in particular when dealing with low speed flows since this behaviour is exacerbated approaching the incompressibility limit fixes for the excess of numerical dissipation of these schemes have been proposed by several authors in the context of different numerical methods see for example weiss and smith 1995 in this work a simple modification of the dissipation term of the low mach preconditioned roe scheme proposed by weiss and smith is considered the aim is to reduce further the amount of numerical dissipation with the intent of improving the results of udns a spatial dg discretization coupled with a linearly implicit rosenbrock type time integrator is here considered as a numerical framework perfectly suited for the assessment and comparison of different numerical flux functions results on canonical turbulent flow problems as the taylor green vortex and the flow in a straight sided channel are presented the improved accuracy of the proposed flux function is demonstrated the new low dissipation flux can be useful also in the context of standard lower order finite volume methods

a second order time accurate finite volume method for unsteady incompressible flow on hybrid unstructured grids a new second order time accurate fractional step method for solving unsteady incompressible navier stokes equations on hybrid unstructured grids is presented the nonstaggered grid method originally developed by rhie and chow 1983 aiaa j 21 1525 for steady flow and further extended by zang et al 1994 j comput phys 114 18 to unsteady flow on structured grids is employed in the present study to enforce mass conservation on hybrid unstructured grids the pressure and cartesian velocity components are defined at the center of each cell while the face normal velocities are defined at the mid points of the corresponding cell faces a second order fully implicit time advancement scheme is used for time integration and the resulting nonlinear equations are linearized without losing the overall time accuracy both the momentum and poisson equations are integrated with the finite volume method and the flow variables at the cell face are obtained using an interpolation scheme independent of cell shape the present numerical method is applied to four different benchmark problems and proves to be accurate and efficient

assessment of three preconditioning schemes for solution of the two dimensional euler equations at low mach number flows summary three preconditioners proposed by eriksson choi and merkel and turkel are implemented in a 2d upwind euler flow solver on unstructured meshes the mathematical formulations of these preconditioning schemes for different sets of primitive variables are drawn and their eigenvalues and eigenvectors are compared with each other for this purpose these preconditioning schemes are expressed in a unified formulation a cell centered finite volume roe s method is used for the discretization of the preconditioned euler equations the accuracy and performance of these preconditioning schemes are examined by computing steady low mach number flows over a naca0012 airfoil and a two element naca4412 4415 airfoil for different conditions the study shows that these preconditioning schemes greatly enhance the accuracy and convergence rate of the solution of low mach number flows the study indicates that the preconditioning methods implemented provide nearly the same results in accuracy however they give different performances in convergence rate it is demonstrated that although the convergence rate of steady solutions is almost independent of the choice of primitive variables and the structure of eigenvectors and their orthogonality the condition number of the system of equations plays an important role and it determines the convergence characteristics of solutions copyright 2011 john wiley sons ltd

computational treatment of source terms in two equation turbulence models the source terms in turbulence models require careful treatment to obtain a stable discretization the choice between implicit and explicit treatment has to be made this can be done either on the basis of individual terms or on the basis of the exact jacobian of the source terms a comparison of both methods shows that the latter is generally applicable and superior to the first approximate method with respect to convergence speed this comes from the possibility of using the multigrid technique with the exact method whereas this is not always possible with the approximate method in principle for robustness a time step restriction for the source terms has to be introduced to prevent the turbulence quantities from becoming negative or infinitely large an approximation of the appropriate time step is calculated practical results however indicate that the time step restriction is not always necessary different two equation turbulence models are investigated confirming the generality of the approach

a free boundary problem for a singular system of differential equations an application to a model of tumor growth first published in transactions of the american mathematical society in volume 355 issue 9 published by the american mathematical society

a multigrid method for natural convective heat transfer with large temperature differences steady state two dimensional solutions to the full compressible navier stokes equations are computed for laminar convective motion of a gas in a square cavity with large horizontal temperature differences results for air are presented the ideal gas law is used and viscosity is given by sutherland s law an accurate low mach number solver is developed hereby an explicit third order discretization for the convective part and a line implicit central discretization for the acoustic part and for the diffusive part are used the semi implicit line method is formulated in multistage form multigrid is used as acceleration technique a convergence behaviour is obtained which is independent of grid size grid aspect ratio mach number and rayleigh number grid converged results are shown for rayleigh numbers between 102 and 107

alleviation of cancellation problem of preconditioned navier stokes equations an approach to alleviate the cancellation problem of preconditioned navier stokes equations is proposed adiabatic laminar viscous flows around a circular cylinder are calculated at different mach numbers it is shown that a redefinition of total enthalpy to reduce the magnitude of total enthalpy can alleviate the cancellation problem for adiabatic laminar flows at low mach numbers

a conservative discrete compatibility constraint low mach pressure correction algorithm for time accurate simulations of variable density flows in this paper we develop the discrete compatibility constraint pressure correction algorithm for transient simulations of variable density flows at low mach numbers the constraint for the velocity field is constructed from a combination of the discrete equations of continuity and scalar e g energy transport imposing that the newly predicted state must be compatible in agreement with the equation of state this way mass and scalar conservation are guaranteed and the equation of state is exactly fulfilled at every time step for comparison reasons two other types of well known pressure correction algorithms are also used the first class denoted as continuity constraint pressure correction is based on a constraint for the velocity field that is derived solely from the continuity equation the second class denoted as analytical compatibility constraint pressure correction constructs the constraint from an analytical combination of the material derivative of the equation of state and the continuity and scalar equations the algorithms are tested for three example fluid configurations a single fluid ideal gas a two fluid inert mixture and a two fluid reacting mixture the latter is special in the sense that the equation of state is non linear and not everywhere differentiable the continuity constraint pressure correction algorithm yields unstable solutions if density ratios are high the analytical compatibility constraint pressure correction algorithm yields stable results but the predicted states do not correspond to the equation of state the discrete compatibility constraint pressure correction algorithm performs well on all test cases the simulation results are stable and exactly match the equation of state

the momentum interpolation method based on the time marching algorithm for all speed flows the time marching approach has clear physical meaning and strict mathematical nature and has been applied in computation of compressible flows widely and extended to many uniform algorithms for all speed flows remedy for its weakness in the problem of checkerboard decoupling of pressure field for incompressible flows is envisaged with the time marching momentum interpolation method mim taken into account in this paper existing preconditioning methods for suppressing decoupling and time marching mim are analyzed for this purpose and algorithms of time marching mim are proposed for steady and unsteady flows and for all speed flows asymptotic analysis shows that the supposed time marching mim has at least a third order accuracy better than the existing time marching coupling methods which only have an accuracy of the same order as the adopted scheme has effects of the time step sizes on the ability of the time marching mim to suppress the checkerboard pressure decoupling are particularly discussed in terms of the dual time stepping approach and it is revealed how the decreased sizes of either the pseudo or physical time step increases the possibility of decoupling and how choi s modification in which the history of the interface velocity is decided by itself instead of the arithmetic average of the velocities on its adjacent nodes removes the unphysical pressure oscillation with small size of the physical time step but leads to divergence with the pseudo time step as well as a remedy for the pseudo time step such methods are recommended as implicit methods and the local time step method with a proposed modification of the time marching mim preventing accuracy loss due to very large time step size numerical experiments support the theoretical analyses and show the validity of the time marching mim proposed

numerical study of the flow in a three dimensional thermally driven cavity solutions for the fully compressible navier stokes equations are presented for the flow and temperature fields in a cubic cavity with large horizontal temperature differences the ideal gas approximation for air is assumed and viscosity is computed using sutherland s law the three dimensional case forms an extension of previous studies performed on a two dimensional square cavity the influence of imposed boundary conditions in the third dimension is investigated as a numerical experiment comparison is made between convergence rates in case of periodic and free slip boundary conditions results with no slip boundary conditions are presented as well the effect of the rayleigh number is studied results are computed using a finite volume method on a structured collocated grid an explicit third order discretization for the convective part and an implicit central discretization for the acoustic part and for the diffusive part are used to stabilize the scheme an artificial dissipation term for the pressure and the temperature is introduced the discrete equations are solved using a time marching method with restrictions on the timestep corresponding to the explicit parts of the solver multigrid is used as acceleration technique

simultaneous solution algorithms for eulerian eulerian gas solid flow models stability analysis and convergence behaviour of a point and a plane solver simultaneous solution algorithms for eulerian eulerian gas solid flow models are presented and their stability analyzed the integration algorithms are based on dual time stepping with fourth order runge kutta in pseudo time the domain is solved point or plane wise the discretization of the inviscid terms is based on a low mach limit of the multi phase preconditioned advection upstream splitting method mp ausmp the numerical stability of the simultaneous solution algorithms is analyzed in 2d with the fourier method stability results are compared with the convergence behaviour of 3d riser simulations the impact of the grid aspect ratio preconditioning artificial dissipation and the treatment of the source terms is investigated a particular advantage of the simultaneous solution algorithms is that they allow a fully implicit treatment of the source terms which are of crucial importance for the eulerian eulerian gas solid flow models and their solution the numerical stability of the optimal simultaneous solution algorithm is analyzed for different solids volume fractions and gas solid slip velocities furthermore the effect of the grid resolution on the convergence behaviour and the simulation results is investigated finally simulations of the bottom zone of a pilot scale riser with a side solids inlet are experimentally validated

a three dimensional incompressible navier stokes flow solver using primitive variables an implicit finite difference computer code has been developed to solve the incompressible navier stokes equations in a three dimensional curvilinear coordinate system the pressure field solution is based on the pseudocompressibility approach in which a time derivative pressure term is introduced into the mass conservation equation the solution procedure employs an implicit approximate factorization scheme the reynolds stresses which are uncoupled from the implicit scheme are lagged by one time step to facilitate implementing various levels of the turbulence model test problems for external and internal flows are computer and the results are compared with existing experimental data the application of this technique for general three dimensional problems is then demonstrated

a coupled implicit method for chemical non equilibrium flows at all speeds a time accurate coupled solution procedure is described for the chemical nonequilibrium navier stokes equations over a wide range of mach numbers this method employs the strong conservation form of the governing equations but uses primitive variables p g u v h y i as unknowns real gas properties and nonequilibrium chemistry are considered numerical tests include steady convergent divergent nozzle flows with air dissociation recombination chemistry dump combustor flows withn pentane air chemistry and nonreacting unsteady driven cavity flows numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for mach numbers ranging from the incompressible limit to supersonic speeds c 1993 academic press inc

an improved unsteady unstructured artificial compressibility finite volume scheme for viscous incompressible flows part ii application in part i of this paper a preconditioned artificial compressibility scheme was developed for modelling laminar steady state and transient incompressible flows for a wide range of reynolds and rayleigh numbers in this part several examples of laminar incompressible problems are solved and discussed the influence of various ac parameters on robustness and convergence rates are assessed for a complex category of problems it is shown that the scheme developed in part i is an accurate robust and easy to use method for solving incompressible laminar flow problems over a wide range of flow regimes copyright 2002 john wiley sons ltd

analysis of a mathematical model of the growth of necrotic tumors abstract in this paper we study a model of necrotic tumor growth the tumor comprises necrotic cells which occupy a radially symmetric core and life proliferating cells which occupy a radially symmetric shell adjacent to the core the proliferating cells receive nutrients through diffusion from the outer boundary as well as by means of blood flow through a network of capillary vessels the mathematical model describes the evolution of the nutrient concentration between the boundary of the necrotic core r t and the outer boundary of the tumor r r t within the core itself the concentration is a constant nec a level under which life cells cannot be sustained both of the surfaces r t and r r t are free boundaries which are unknown in advance under some assumptions on the parameters we prove that i there exists a stationary solution with radii r s r r s ii for any initial data near the stationary solution the time dependent model has a unique solution r t with free boundaries r t r r t and iii t s and r t r s as t

implicit heat flux correction based immersed boundary finite volume method for thermal flows with neumann boundary conditions abstract in the frameworks of immersed boundary method ibm and finite volume method fvm an implicit heat flux correction based ib fvm is proposed for thermal flows with neumann boundary conditions with the use of a fractional step technique the preconditioned navier stokes n s equations are solved by the fvm to obtain the intermediate solution in the prediction step and the heat flux is corrected by enforcing the neumann condition in the correction step different from existing ibms the cell face centers are defined as the eulerian points due to the heat flux computation at each face in the fvm the neumann condition is implemented in such a way that the interpolated temperature gradient is equal to the specified boundary value at the same point when the corrected gradient field is interpolated from the face centers to the lagrangian points to achieve an implicit algorithm the temperature derivative corrections at the lagrangian points are set as unknowns and a system of algebraic equations is established by constructing hybrid thin plate splines tps interpolation delta function distribution in the derivative interpolation process the much more accurate tps is introduced because the use of cosine delta function yields a less accurate solution after the distribution process the heat flux correction of a fluid cell is evaluated by using the solved temperature derivative corrections at the face centers but that of a solid cell is calculated by using their additive inverses to supplement the same amount of heat flux into the solid domain as that flowing into the fluid domain across the boundary finally the heat flux of a cell is corrected by adding the correction to the intermediate value and the corrected heat flux is utilized to solve the n s equations in the prediction step as compared with the available implicit ibms for neumann conditions the present method avoids the introduction of auxiliary layers of lagrangian points as well as the approximate conversion from the neumann to dirichlet condition and thus is suitable for an arbitrary geometry the proposed method is verified by simulating several benchmark thermal flows with neumann conditions the natural convection in an annulus and the steady or unsteady forced convection over a stationary or oscillating cylinder all the computed results agree well with the literature data

unified formulation for compressible and incompressible flows by using multi integrated moments ii multi dimensional version for compressible and incompressible flows following our previous paper on a novel finite volume formulation for computing flows of any mach number we present the multi dimensional extension of the method in this paper treating two kinds of averages which are generically called moments and defined as the volume integrated average via and the surface integrated average sia in this paper as the prognostic variables makes the present method different from the conventional finite volume method where only via is the basic variable the resulting discretization approach which is a type of the cip multi moment finite volume method and called vsiam3 volume surface integrated average based multi moment method is combined with a pressure based projection formulation for the time integration to enable the simulations for both compressible and incompressible flows the numerical algorithm for multi dimensions will be reported in this paper numerical experiments with flows of a wide range mach numbers will be also presented

a mach uniform algorithm coupled versus segregated approach a mach uniform algorithm is an algorithm with a good convergence rate for any level of the mach number in this paper the severe time step restriction for low speed flows is removed by treating the acoustic and diffusive terms implicitly after identification of these terms in the conservative set we end up with a semi implicit system the way to solve this system can be chosen three different solution techniques are presented a fully coupled algorithm the coupled pressure and temperature correction algorithm k nerinckx j vierendeels e dick mach uniformity through the coupled pressure and temperature correction algorithm journal of computational physics 206 2005 597 623 and a fully segregated pressure correction algorithm we analyse the convergence behavior of the considered algorithms for some typical flow problems moreover a fourier stability analysis is done for inviscid flow the fully segregated and the fully coupled algorithm need about as much time steps to reach steady state therefore the more segregation is introduced the faster the calculation can be done in case of heat transfer the fully segregated pressure correction algorithm suffers from a diffusive time step limit this is not the case for the semi segregated coupled pressure and temperature correction algorithm finally when the gravity terms play an important role only the fully coupled algorithm can avoid an additional time step restriction

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

a high resolution pressure based algorithm for fluid flow at all speeds abstract a new collocated finite volume based solution procedure for predicting viscous compressible and incompressible flows is presented the technique is equally applicable in the subsonic transonic and supersonic regimes pressure is selected as a dependent variable in preference to density because changes in pressure are significant at all speeds as opposed to variations in density which become very small at low mach numbers the newly developed algorithm has two new features i the use of the normalized variable and space formulation nvsf methodology to bound the convective fluxes and ii the use of a high resolution scheme in calculating interface density values to enhance the shock capturing property of the algorithm the virtues of the newly developed method are demonstrated by solving a wide range of flows spanning the subsonic transonic and supersonic spectrum results obtained indicate higher accuracy when calculating interface density values using a high resolution scheme

short note cancellation problem of preconditioning method at low mach numbers the effects of cancellation errors on the convergence characteristics of preconditioned navier stokes equations at low mach numbers are analyzed laminar viscous flows around a circular cylinder are calculated at different mach numbers it is shown that the cancellation error in the energy equation grows faster than those in the other equations as the mach number decreases it is also shown that the cancellation problem of the energy equation is due to the off diagonal element that is related to a pressure change in the preconditioner

statistical mechanics of low density parity check codes we review recent theoretical progress on the statistical mechanics of error correcting codes focusing on low density parity check ldpc codes in general and on gallager and mackay neal codes in particular by exploiting the relation between ldpc codes and ising spin systems with multispin interactions one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions corresponding to dynamical and thermodynamical transitions respectively as well as the behaviour of error exponents averaged over the corresponding code ensemble as a function of channel noise we also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature and show how these methods can be generalized to include other channel types and related communication problems

effects of condition number on preconditioning for low mach number flows the effects of the condition number on convergence characteristics and solution quality for the preconditioned navier stokes equations are studied a general approach to the construction of preconditioning parameters is proposed to account for the effects of the condition number on these parameters to verify this technique laminar flows past a circular cylinder at reynolds numbers of 20 and 40 and laminar flows past a naca0012 airfoil at reynolds numbers of 2500 and 5000 are solved it is shown that the condition number has effects on the convergence characteristics and solution qualities and also that a condition number exists that optimizes the convergence characteristics and solution quality

a multigrid semi implicit line method for viscous incompressible and low mach number flows on high aspect ratio grids abstract discretization of viscous incompressible and viscous low mach number flows often leads to a system of equations which is very difficult to solve there are two reasons first the use of high aspect ratio grids results in a very numerically anisotropic behaviour of the diffusive and acoustic terms and second in low mach number flow the ratio of the convective and acoustic eigenvalues of the inviscid system becomes very high we implemented an ausm based discretization method using an explicit third order discretization for the convective part and a line implicit central discretization for the acoustic part and for the diffusive part the lines are chosen in the direction of the grid points with shortest connection the preconditioned semi implicit line method is used in multistage form because of the explicit third order discretization of the convective part multigrid is used as an acceleration technique it is shown that the convergence is very good independent of grid aspect ratio and mach number

stability analysis of preconditioned approximations of the euler equations on unstructured meshes this paper analyses the stability of a discretisation of the euler equations on 3d unstructured grids using an edge based data structure first order characteristic smoothing a block jacobi preconditioner and runge kutta timemarching this is motivated by multigrid navier stokes calculations in which this inviscid discretisation is the dominant component on coarse grids the analysis uses algebraic stability theory which allows at worst a bounded linear growth in a suitably defined perturbation energy provided the range of values of the preconditioned spatial operator lies within the stability region of the runge kutta algorithm the analysis also includes consideration of the effect of solid wall boundary conditions and the addition of a low mach number preconditioner to accelerate compressible flows in which the mach number is very low in a significant portion of the flow numerical results for both inviscid and viscous applications confirm the effectiveness of the numerical algorithm and show that the analysis provides accurate stability bounds

development of low diffusion flux splitting methods for dense gas solid flows the development of a class of low diffusion upwinding methods for computing dense gas solid flows is presented in this work an artificial compressibility low mach preconditioning strategy is developed for a hyperbolic two phase flow equation system consisting of separate solids and gas momentum and continuity equations the eigenvalues of this system are used to devise extensions of the ausm 1 and ldfss 2 flux splitting methods that provide high resolution capturing of bubble growth and collapse in gas solid fluidized beds applications to several problems in fluidization are presented

the nishimori line and bayesian statistics the nishimori line is a line or hypersurface in the parameter space of systems with quenched disorder where simple expressions of the averages of physical quantities over the quenched random variables are obtained it has been playing an important role in the theoretical studies of the random frustrated systems since its discovery in around 1980 in this paper an interpretation of the nishimori line from the viewpoint of statistical information processing is developed our main aim is the reconstruction of the whole theory of the nishimori line from the viewpoint of bayesian statistics or almost equivalently from the viewpoint of the theory of error correcting codes as a byproduct of the interpretation counterparts of the nishimori line in models without gauge invariance are given we also discussed the issues on the finite temperature decoding of error correcting codes and clarify the role of gauge invariance in this topic

low diffusion flux splitting methods for flows at all speeds methods for extending the advective upwind splitting method ausm family of low diffusion flux splitting schemes to operate effectively at all flow speeds are developed the extensions developed are designed for use with time derivative preconditioning and are based on the idea that the speed of sound should cease to be an important scaling parameter for the diffusive contributions to the interface flux as the mach number becomes small using this criterion alternative definitions for the interface mach numbers are developed and methods for ensuring pressure velocity coupling at low speeds are formulated results are presented for inviscid flows through a channel at various mach numbers developing viscous flow in a two dimensional duct driven cavity flows at various mach and reynolds numbers flow over a backward facing step and hydrogen nitrogen mixing layers

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

bifurcation for a free boundary problem modeling the growth of multi layer tumors abstract in this paper we study bifurcations for a free boundary problem modeling the growth of multi layer tumors under the action of inhibitors an important feature of this problem is that the surface tension effect of the free boundary is taken into account by reducing this problem into an abstract bifurcation equation in a banach space overcoming some technical difficulties and finally using the crandall rabinowitz bifurcation theorem we prove that this problem has infinitely many branches of bifurcation solutions bifurcating from the flat solution

an all speed roe type scheme and its asymptotic analysis of low mach number behaviour a new scheme all speed roe scheme was proposed for all speed flows compared with traditional preconditioned roe scheme all speed roe scheme changes non linear eigenvalues in the numerical dissipation terms of roe type schemes with an asymptotic analysis the low mach number behaviour of the scheme is studied theoretically in two ways in one way all speed roe scheme is regarded as finite magnification of low speed roe scheme in the low mach number limit in the other way a general form of all speed roe scheme is analyzed both ways demonstrate that all speed roe scheme has the same low mach number behaviour as the original governing equation in the continuous case which includes three important features pressure variation scales with the square of the mach number the zero order velocity field is subject to a divergence constraint and the second order pressure satisfies a poisson type equation in the case of constant entropy the analysis also leads to an unexpected conclusion that the velocity filed computed by traditional preconditioned roe scheme does not satisfy the divergence constraint as the mach number vanishes moreover the analysis explains the reason of checkerboard decoupling and shows that momentum interpolation method provides a similar mechanism as traditional preconditioned roe scheme inherently possesses to suppress checkerboard decoupling in the end general rulers for modifying non linear eigenvalues are obtained finally several numerical experiments are provided to support the theoretical analysis all speed roe scheme has a sound foundation and is expected to be widely studied and applied to all speed flow calculations

a flux vector splitting scheme for low mach number flows in preconditioning method abstract the stiffness of euler equations system increases with the decreasing of mach number which results in poor convergence when solving steady flow problems numerically in order to accelerate the convergence a preconditioning method is proposed a flux vector splitting scheme is derived from the classic steger warming scheme and the roe flux difference splitting scheme and preconditioned systems developed for the two schemes separately numerical results are presented and it is shown that flux vector splitting scheme can be preconditioned as successfully as flux difference splitting and exhibits similar convergence acceleration and accurate solution

improving the low mach number steady state convergence of the cascaded lattice boltzmann method by preconditioning abstract cascaded lattice boltzmann method lbm involves the use of central moments in a multiple relaxation time formulation in prescribing the collision step when the goal is to simulate low mach number stationary flows the greater the disparity between the magnitude of fluid speed and the sound speed the higher is the numerical stiffness which results in relatively large number of time steps for convergence of the lbm one way to improve the steady state convergence of the scheme is to precondition the cascaded lbm which reduces the disparities between the characteristic speeds or equivalently those between the eigenvalues of the system in this paper we present a new preconditioned two dimensional cascaded lbm where a preconditioning parameter is introduced into the equilibrium moments as well as the forcing terms particular focus is given to preconditioning differently the moments due to forcing at first and second orders so as to avoid any spurious effects in the emergent macroscopic equations a chapman enskog analysis performed on this approach shows consistency to the preconditioned navier stokes equations this modified central moment based scheme is then validated for accuracy by comparison against prior analytical or numerical results for certain benchmark problems including those involving spatially variable body forces finally significant steady state convergence acceleration of the preconditioned cascaded lbm is demonstrated for a set of characteristic parameters

an efficient parallel unstructured multigrid preconditioned implicit method for simulating 3d unsteady compressible flows with moving objects this paper presents the development and validation of a new parallel unstructured multi grid preconditioned implicit method for the simulation of three dimensional 3d unsteady compressible flows using a so called immersed membrane method imm g h xia y zhao j h yeo an immersed membrane method for simulation of flui structure interaction in bio fluid flows in 1st international bioengineering conference ibec 2004 08 10 september 2004 the novel feature of the method presented is that it employs a unique combination of a parallel multi grid scheme with low mach number preconditioning and the imm so that 3d unsteady low mach number flows with arbitrarily moving objects can be efficiently simulated

analysis of a mathematical model for tumor growth under indirect effect of inhibitors with time delay in proliferation in this paper a mathematical model for tumor growth with time delay in proliferation under indirect effect of inhibitor is studied the delay represents the time taken for cells to undergo mitosis nonnegativity of solutions is investigated the steady state analysis is presented with respect to the magnitude of the delay existence of hopf bifurcation is proved for some parameter values local and global stability of the stationary solutions are proved for other ones the analysis of the effect of inhibitor s parameters on tumor s growth is presented the results show that dynamical behavior of solutions of this model is similar to that of solutions for corresponding non retarded problems for some parameter values

local preconditioning and variational multiscale stabilization for euler compressible steady flow abstract this paper introduces a preconditioned variational multiscale stabilization p vms method for compressible flows in this introductory paper we focus on inviscid flow and steady state problems the euler equations are solved on fully unstructured grids and discretized using the finite element method the p vms method can be decomposed into three parts first a local preconditioner is applied to the continuous equations to reduce the stiffness while covering a wide range of mach numbers then the resulting preconditioned system is discretized in space using finite elements and stabilized with a variational multiscale stabilization method adapted for the preconditioned equations in this paper the solution is advanced in time using a fully explicit time discretization although p vms is general and can be applied to fully implicit solvers the proposed method is assessed by comparing convergence and accuracy of the solutions between the non preconditioned and preconditioned cases in particular for van leer lee roe s 1991 and choi merkle s 1993 preconditioners in some selected examples covering a large range of mach numbers

preconditioned dual time procedures and its application to simulating the flow with cavitations preconditioning technology is a method that can unify the method of cfd for high speed low speed compressible and incompressible flows in the flow with cavitations incompressible liquid and compressible vapor coexist the phase transition in the flow results in complex thermophysical processes in this paper based on the primitive variables pressure velocity and enthalpy a preconditioned dual time procedures is established which can deal with unsteady flow field with cavitations the energy equation is adopted to replace the traditional cavitational model roe s scheme is used to capture the disconnected surface the examples indicate that this method can be used to capture the unsteady cavity in the flow field

mach uniformity through the coupled pressure and temperature correction algorithm we present a new type of algorithm the coupled pressure and temperature correction algorithm it is situated in between the fully coupled and the fully segregated approach and is constructed such that mach uniform accuracy and efficiency are obtained the essential idea is the separation of the convective and the acoustic thermodynamic phenomena a convective predictor is followed by an acoustic thermodynamic corrector for a general case the corrector consists of a coupled solution of the energy and the continuity equations for both pressure and temperature corrections for the special case of an adiabatic perfect gas flow the algorithm reduces to a fully segregated method with a pressure correction equation based on the energy equation various test cases are considered which confirm that mach uniformity is obtained

a hyperbolic free boundary problem modeling tumor growth asymptotic behavior first published in transactions of the american mathematical society in volume 357 issue 12 published by the american mathematical society

low temperature thermodynamics of random field ising chains exact results the authors consider the random field ferromagnetic ising chain for a class of continuous symmetric probability distributions of the random magnetic fields of a diluted power times exponential type this class of distribution is exactly solvable in the sense that the disorder can be integrated explicitly at any temperature a detailed analysis of the low temperature thermodynamics is presented exact expressions are obtained for the ground state energy the zero temperature entropy and the amplitude of the specific heat which vanishes linearly at low temperature the diluted symmetric binary distribution where the magnetic fields can only assume the values or hb or zero can be viewed as a limiting case of the class of exactly solvable distributions the low temperature physics of this discrete model is investigated in detail including the exponential fall off of the specific heat

extension of harten lax van leer scheme for flows at all speeds the harten lax and van leer with contact restoration hllc scheme has been modified and extended in conjunction with time derivative preconditioning to compute flow problems at all speeds it is found that a simple modification of signal velocities in the hllc scheme based on the eigenvalues of the preconditioned system is only needed to reduce excessive numerical diffusion at the low mach number the modified scheme has been implemented and used to compute a variety of flow problems in both two and three dimensions on unstructured grids numerical results obtained indicate that the modified hllc scheme is accurate robust and efficient for flow calculations across the mach number range istorically numerical algorithms for the solution of the euler and navier stokes equations are classified as either pressure based or density based solution methods the pressurebased methods originally developed and well suited for incompressible flows are typically based on the pressure correction techniques they usually use a staggered grid and solve the governing equations in a segregated manner the density based methods originally developed and robust for compressible flows use time arching procedures to solve the hyperbolic system of governing equations in a coupled manner in general density based methods are not suitable for efficiently solving low mach number or incompressible flow problems because of large ratio of acoustic and convective timescales at the low speed flow regimes to alleviate this stiffness and associated convergence problems time derivative preconditioning techniques have been developed and used successfully for solving low machnumber and incompressible flows by many investigators including chorin 1 choi and merkle 2 turkel 3 weiss and smith 4 and dailey and pletcher 5 among others such methods seek to modify the time component of the governing equations so that the convergence can be made independent of mach number this is accomplished by altering the acoustic speeds of the system so that all eigenvalues become of the same order and thus condition number remains bounded independent of the mach number of the flows over the last two decades characteristic based upwind methods have established themselves as the methods of choice for prescribing the numerical fluxes for compressible euler equations when these upwind methods are used to compute the numerical fluxes for the preconditioned euler equations solution accuracy at low speeds can be compromised unless the numerical flux formulation is modified to take into account the eigensystem of the precondi

well posedness and stability of a multi dimensional tumor growth model we study a moving boundary problem modeling the growth of in vitro tumors this problem consists of two elliptic equations describing the distribution of the nutrient and the internal pressure respectively and a first order partial differential equation describing the evolution of the moving boundary an important feature is that the effect of surface tension on the moving boundary is taken into account we show that this problem is locally well posed for a large class of initial data by using analytic semi group theory we also prove that if the surface tension coefficient is larger than a threshold value then the unique flat equilibrium is asymptotically stable whereas in the case this flat equilibrium is unstable

computation of compressible and incompressible flows with a space time stabilized finite element method abstract this paper presents the numerical results of compressible and incompressible flow problems through a unified approach based on a stabilized space time finite element method the numerical approach is continuous in space and discontinuous in time the proposed method starts by the use of a stabilized space time variational formulation which allows the use of the same order interpolation functions for all solution variables the numerical technique is tested through comparison with standard compressible and incompressible flow benchmarks compressible flow cases include 1d and 2d shock problems incompressible flow cases include lid driven cavity flow and flow over a backward facing step computed over a range of r e numbers the results demonstrate high stability and accuracy of the numerical technique over a wide range of flow regimes suggesting straightforward extension to many flow cases not yet investigated

application of an unstructured navier stokes code to prediction of adiabatic effectiveness of endwall flush slot cooling for a stator vane passage a three dimensional unstructured finite volume code developed for rans computations with the artificial compressibility approach is described the code is applied to prediction of adiabatic effectiveness of endwall flush slot cooling for a stator vane passage results obtained with the spalart allmaras and the menter sst turbulence models are presented and discussed in comparison with measurements and with the data computed using the fluent commercial software package

development and validation of navier stokes procedure for turbomachinery unsteady flow an unsteady viscous flow solver based on the runge kutta scheme has been developed three low reynolds number e turbulence models have been assessed for their ability to predict unsteady transitional flow the e model has been modified to incorporate leading edge effects a pseudo time approach has been used to accelerate the numerical algorithm for unsteady flows a sensitivity study has been carried out including the effects of the artificial dissipation the grid density and the physical and pseudo time steps the numerical simulation of the unsteady transitional flow in a compressor cascade has been carried out successfully the numerical solver has been able to prediet major features associated with the wake induced transition on a compressor blade wake induced transitional strip wake induced turbulent strip etc an analysis and an interpretation of the results from the unsteady flow simulation have been carried out to understand additional flow physics associated with the transitional flow

shock stable roe scheme combining entropy fix and rotated riemann solver the roe scheme is an important shock capturing scheme that is known for its good performance however the classical roe scheme suffers from disastrous problems such as shock instability for hyper

preconditioning applied to variable and constant density flows a time derivative preconditioning of the navier stokes equations suitable for both variable and constant density fluids is developed the ideas of low mach number preconditioning and artificial compressibility are combined into a unified approach designed to enhance convergence rates of density based time marching schemes for solving flows of incompressible and variable density fluids at all speeds the preconditioning is coupled with a dual time stepping scheme implemented within an explicit multistage algorithm for solving time accurate flows the resultant time integration scheme is used in conjunction with a finite volume discretization designed for unstructured solution adaptive mesh topologies this method is shown to provide accurate steady state solutions for transonic and low speed flow of variable density fluids the time accurate solution of unsteady incompressible flow is also demonstrated