analysis of an explicit and matrix free fractional step method for incompressible flows in this paper we present the analysis of an explicit and matrix free fractional step method for incompressible flows the presented method can be employed in either conservation or non conservation form the stabilization convergence and conservation aspects of the presented method are discussed a procedure for eliminating the first order error in time introduced by the split is proposed some benchmark steady and unsteady state examples are presented to demonstrate the proposed new aspects of the matrix free scheme

accurate three dimensional lid driven cavity flow a chebyshev collocation method in space is introduced which allows an accurate calculation of three dimensional lid driven cavity flows the time integration is carried out by an adams bashforth backward euler scheme the accuracy of the method relies on the representation of the solution as a superposition of stationary local asymptotic solutions and a residual flow field this way the most severe discontinuities in the boundary conditions which arise along the lines where moving and stationary walls meet are taken care of analytically and thus do not spoil the numerical part of the solution calculations are carried out for no slip boundary conditions at the cavity end walls as well as for periodic end wall conditions in general the spatial accuracy is better than fifth order for rigid end wall conditions the accuracy is reduced near the end walls to o n 3 2 but recovers in the bulk tabulated data are provided for the most interesting flow properties

implicit hybrid upwinding for two phase flow in heterogeneous porous media with buoyancy and capillarity abstract we consider the numerical solution of the partial differential equations governing multiphase flow in porous media for highly nonlinear problems the temporal discretization of choice is often the unconditionally stable fully implicit method however the nonlinear systems often solved with newton s method are difficult to solve thus the computational cost is strongly dependent on the nonlinear convergence rate and enhancing this convergence property is key to speed up subsurface flow simulation we focus on the case of spatially discontinuous capillary pressure between rock regions to efficiently and accurately simulate the flow dynamics in heterogeneous porous media the flux computation combines implicit hybrid upwinding with transmission conditions between different rock regions this leads to a scheme that correctly represents the trapping mechanisms while improving the nonlinear convergence we extend our previous results hamon et al 2016 18 by generalizing the scheme to fully implicit coupled flow and transport to address realistic problems in multiple dimensions the generalized scheme is supported by an analysis of its mathematical properties our multidimensional numerical examples which range from buoyancy driven flow with capillary barriers to viscous dominated flow demonstrate that the implicit hybrid upwinding scheme improves the accuracy compared to the standard phase based upwinding scheme while leading to significant reductions in the number of nonlinear iterations in multiple dimensions

power associative nilalgebras of dimension 9 abstract in 19 authors described some properties about commutative power associative nilalgebras of nilindex 5 here we will get new results about the structure of this class of algebras those results will allow us to prove that every commutative power associative algebra of dimension 9 and nilindex 5 over a field of characteristic different from 2 3 and 5 is solvable consequently the famous albert s conjecture 1 problem 1 1 is setted for dimension 9 and characteristic 0 since the case of dimension 9 and nilindex 5 have already been examined in 27 11 14 and 20

monotonicity considerations for saturated unsaturated subsurface flow it is demonstrated that monotonicity is a sufficient condition to ensure that no new nonphysical local maxima and minima can be produced in the discrete nonlinear unsaturated flow equation monotonicity conditions are derived for various types of weighting for the mobility term the basic discretization is of finite element type but the results can be extended to finite volume discretizations central weightings are only conditionally monotone while upstream weightings are unconditionally monotone sample computations are given for highly heterogeneous problems

on the solvability of the commutative power associative nilalgebras of dimension 6 abstract we prove that commutative power associative nilalgebras of dimension 6 over a field of characteristic 2 3 5 are solvable

nilpotent linear spaces and albert s problem abstract in 8 m a fasoli classified up to conjugation all the maximal vector subspaces of m 4 c in which all the elements are nilpotent matrices this result will allow us to solve albert s problem 5 for commutative power associative c nilalgebras of dimension n and nilindex n 3 in an affirmative way

on discontinuous galerkin methods discontinuous galerkin methods have received considerable attention in recent years for problems in which advection and diffusion terms are present several alternatives for treating the diffusion and advective fluxes have been introduced this report summarizes some of the methods that have been proposed several numerical examples are included in the paper these present discontinuous galerkin solutions of one dimensional problems with a scalar variable results are presented for diffusion reaction problems and advection diffusion problems we discuss the performance of various formulations with respect to accuracy as well as stability of the method copyright 2003 john wiley sons ltd

the characteristic based split cbs scheme a unified approach to fluid dynamics this paper presents a comprehensive overview of the characteristic based methods and characteristic based split cbs scheme the practical difficulties of employing the original characteristic schemes are discussed the important features of the cbs scheme are brought out by studying several problems of compressible and incompressible flows all special consideration necessary for solving these problems are thoroughly discussed the cbs scheme is presented in such a way that any interested researcher should be able to develop a code using the information provided several invicid and viscous flow examples are also provided to demonstrate the unified cbs approach for sample two dimensional codes input files and instructions the readers are referred to www nithiarasu co uk copyright 2006 john wiley sons ltd

on a class of commutative power associative nilalgebras abstract we prove that commutative power associative nilalgebras of nilindex n and dimension n are nilpotent of index n we find a necessary and sufficient condition for such an algebra to be a jordan algebra and give all corresponding isomorphism classes

a multi dimensional high order discontinuous galerkin method based on gas kinetic theory for viscous flow computations this paper presents a high order discontinuous galerkin dg method based on a multi dimensional gas kinetic evolution model for viscous flow computations generally the dg methods for equations with higher order derivatives must transform the equations into a first order system in order to avoid the so called non conforming problem in the traditional dg framework the inviscid and viscous fluxes are numerically treated differently differently from the traditional dg approaches the current method adopts a kinetic evolution model for both inviscid and viscous flux evaluations uniformly by using a multi dimensional gas kinetic formulation we can obtain a spatial and temporal dependent gas distribution function for the flux integration inside the cell and at the cell interface which is distinguishable from the gaussian quadrature point flux evaluation in the traditional dg method besides the initial higher order non equilibrium states inside each control volume a linear least square lls method is used for the reconstruction of smooth distributions of macroscopic flow variables around each cell interface in order to construct the corresponding equilibrium state instead of separating the space and time integrations and using the multistage runge kutta time stepping method for time accuracy the current method integrates the flux function in space and time analytically which subsequently saves the computational time many test cases in two and three dimensions which include high mach number compressible viscous and heat conducting flows and the low speed high reynolds number laminar flows are presented to demonstrate the performance of the current scheme

on monotonicity of difference schemes for computational physics criteria are developed for monotonicity of linear as well as nonlinear difference schemes associated with the numerical analysis of systems of partial differential equations integrodifferential equations etc difference schemes are converted into variational forms that satisfy the boundary maximum principle and also allow the investigation of monotonicity for nonlinear operators using linear patterns sufficient conditions are provided to review the monotonicity of single and coupled difference schemes necessary as well as necessary and sufficient conditions for monotonicity of explicit schemes are also developed the notion of submonotone difference schemes is considered and the associated criteria are developed we discuss the interrelationship between monotonicity submonotonicity and stability some known schemes serve as examples demonstrating the implementation of the developed approaches among these examples we describe the possibility that stable schemes such as total variation diminishing tvd as well as monotonicity preserving can produce spurious oscillations

a generalized galerkin method for steady convection diffusion problems with application to quadratic shape function elements abstract a generalization of the standard galerkin finite element method is considered to enable it to deal successfully with steady convection diffusion problems the proposed method employs a generalized governing equation which is obtained by subtracting from the original differential equation the scalar product of its gradient by a vector of free parameters associated with each of the coordinate directions the generalized equation is successively discretized by the standard bubnov galerkin finite element method the effectiveness of the method is illustrated for the case of quadratic local interpolations in one and two space dimensions

on solvability of noncommutative power associative nilalgebras abstract we show that noncommutative power associative nilalgebras of finite dimension n and nilindex k are solvable if k n 1 or k n for any given integer n 2 we present an example of a power associative nilalgebra of dimension n and nilindex n 1 which is not solvable this implies a power associative nilalgebra of dimension n and nilindex k need not be solvable if k n

a particle method for history dependent materials abstract a broad class of engineering problems including penetration impact and large rotations of solid bodies causes severe numerical problems for these problems the constitutive equations are history dependent so material points must be followed this is difficult to implement in a eulerian scheme on the other hand purely lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement remeshing prevents the lockup and tangling but then interpolation must be performed for history dependent variables a process which can introduce errors proposed here is an extension of the particle in cell method in which particles are interpreted to be material points that are followed through the complete loading process a fixed eulerian grid provides the means for determining a spatial gradient because the grid can also be interpreted as an updated lagrangian frame the usual convection term in the acceleration associated with eulerian formulations does not appear with the use of maps between material points and the grid the advantages of both eulerian and lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced also it is shown that impact with no slip is handled without any special algorithm for bodies governed by elasticity and strain hardening plasticity

adaptive moving grid methods for two phase flow in porous media a b s t r a c t in this paper we present an application of the moving mesh method for approximating numerical solutions of the two phase flow model in porous media the numerical schemes combine a mixed finite element method and a finite volume method which can handle the nonlinearities of the governing equations in an efficient way the adaptive moving grid method is then used to distribute more grid points near the sharp interfaces which enables us to obtain accurate numerical solutions with fewer computational resources the numerical experiments indicate that the proposed moving mesh strategy could be an effective way to approximate two phase flows in porous media

a hybrid discontinuous galerkin scheme for multi scale kinetic equations abstract we develop a multi dimensional hybrid discontinuous galerkin method for multi scale kinetic equations this method is based on moment realizability matrices a concept introduced by d levermore w morokoff and b nadiga in 32 and used in 26 for one dimensional problem the main issue addressed in this paper is to provide a simple indicator to select the most appropriate model and to apply a compact numerical scheme to reduce the interface region between different models we also construct a numerical flux for the fluid model obtained as the asymptotic limit of the flux of the kinetic equation finally we perform several numerical simulations for time evolution and stationary problems

a multiscale discontinuous galerkin method with the computational structure of a continuous galerkin method proliferation of degrees of freedom has plagued discontinuous galerkin methodology from its inception over 30 years ago this paper develops a new computational formulation that combines the advantages of discontinuous galerkin methods with the data structure of their continuous galerkin counterparts the new method uses local element wise problems to project a continuous finite element space into a given discontinuous space and then applies a discontinuous galerkin formulation the projection leads to parameterization of the discontinuous degrees of freedom by their continuous counterparts and has a variational multiscale interpretation this significantly reduces the computational burden and at the same time little or no degradation of the solution occurs in fact the new method produces improved solutions compared with the traditional discontinuous galerkin method in some situations

discrete unified gas kinetic scheme for all knudsen number flows low speed isothermal case based on the boltzmann bgk bhatnagar gross krook equation in this paper a discrete unified gas kinetic scheme dugks is developed for low speed isothermal flows the dugks is a finite volume scheme with the discretization of particle velocity space after the introduction of two auxiliary distribution functions with the inclusion of collision effect the dugks becomes a fully explicit scheme for the update of distribution function furthermore the scheme is an asymptotic preserving method where the time step is only determined by the courant friedricks lewy condition in the continuum limit numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current dugks the comparison between the dugks and the well defined lattice boltzmann equation method d2q9 is presented as well

an element wise locally conservative galerkin lcg method for solving diffusion and convection diffusion problems an element wise locally conservative galerkin lcg method is employed to solve the conservation equations of diffusion and convection diffusion this approach allows the system of simultaneous equations to be solved over each element thus the traditional assembly of elemental contributions into a global matrix system is avoided this simplifies the calculation procedure over the standard global continuous galerkin method in addition to explicitly establishing element wise flux conservation in the lcg method elements are treated as sub domains with weakly imposed neumann boundary conditions the lcg method obtains a continuous and unique nodal solution from the surrounding element contributions via averaging it is also shown in this paper that the proposed lcg method is identical to the standard global galerkin gg method at both steady and unsteady states for an inside node thus the method has all the advantages of the standard gg method while explicitly conserving fluxes over each element several problems of diffusion and convection diffusion are solved on both structured and unstructured grids to demonstrate the accuracy and robustness of the lcg method both linear and quadratic elements are used in the calculations for convection dominated problems petrov galerkin weighting and high order characteristic based temporal schemes have been implemented into the lcg formulation

high order accurate time stepping schemes for convection diffusion problems the paper discusses the formulation of high order accurate time stepping schemes for transient convection diffusion problems to be combined with finite element methods of the least squares type for a stable discretization of highly convective problems pade approximations of the exponential function are considered for deriving multi stage time integration schemes involving first time derivatives only thus easier to implement in conjunction with c0 finite elements than standard time stepping schemes which incorporate higher order time derivatives after a brief discussion of the stability and accuracy properties of the multi stage pade schemes and having underlined the similarity between pade and runge kutta methods the paper closes with the presentation of illustrative examples which indicate the effectiveness of the proposed methods

a stable second order partitioned iterative scheme for freely vibrating low mass bluff bodies in a uniform flow abstract we present a stable partitioned iterative scheme for solving fluid body interaction problems at low structure to fluid mass ratio the scheme relies on the so called nonlinear interface force correction based on aitken s extrapolation process to stabilize the coupled partitioned system employing an arbitrary lagrangian eulerian finite element framework approximate interface force correction is constructed through subiterations to account for the missing effects of off diagonal jacobian terms in the partitioned staggered scheme through the generalized aitken s geometric extrapolation process with a dynamic stabilization parameter the interface corrections allow to satisfy the force equilibrium with arbitrary accuracy while expanding the scope of partitioned iterative schemes for fluid structure interaction with strong added mass effects to assess the proposed iterative scheme against the standard strong coupling effects of mass ratio are investigated for a freely vibrating circular cylinder we show that our second order scheme is stable for low mass density ratio and hence is able to handle strong added mass effects the numerical stability and robustness of the scheme is then demonstrated for a new application of tandem square cylinder undergoing complex wake induced vibration and galloping

flip a method for adaptively zoned particle in cell calculations of fluid flows in two dimensions a method is presented for calculating fluid flow in two dimensions using a full particle in cell representation on an adaptively zoned grid the method has many interesting properties among them an almost total absence of numerical dissipation and the ability to represent large variations in the data the method is described using a standard formalism and its properties are illustrated by supersonic flow over a step and the interaction of a shock with a thin foil

conservation properties for the galerkin and stabilised forms of the advection diffusion and incompressible navier stokes equations abstract a common criticism of continuous galerkin finite element methods is their perceived lack of conservation this may in fact be true for incompressible flows when advective rather than conservative weak forms are employed however advective forms are often preferred on grounds of accuracy despite violation of conservation it is shown here that this deficiency can be easily remedied and conservative procedures for advective forms can be developed from multiscale concepts as a result conservative stabilised finite element procedures are presented for the advection diffusion and incompressible navier stokes equations

a third order gas kinetic cpr method for the euler and navier stokes equations on triangular meshes abstract a third order accurate gas kinetic scheme based on the correction procedure via reconstruction cpr framework is developed for the euler and navier stokes equations on triangular meshes the scheme combines the accuracy and efficiency of the cpr formulation with the multidimensional characteristics and robustness of the gas kinetic flux solver comparing with high order finite volume gas kinetic methods the current scheme is more compact and efficient by avoiding wide stencils on unstructured meshes unlike the traditional cpr method where the inviscid and viscous terms are treated differently the inviscid and viscous fluxes in the current scheme are coupled and computed uniformly through the kinetic evolution model in addition the present scheme adopts a fully coupled spatial and temporal gas distribution function for the flux evaluation achieving high order accuracy in both space and time within a single step numerical tests with a wide range of flow problems from nearly incompressible to supersonic flows with strong shocks for both inviscid and viscous problems demonstrate the high accuracy and efficiency of the present scheme

the continuous galerkin method is locally conservative we examine the conservation law structure of the continuous galerkin method we employ the scalar advection diffusion equation as a model problem for this purpose but our results are quite general and apply to time dependent nonlinear systems as well in addition to global conservation laws we establish local conservation laws which pertain to subdomains consisting of a union of elements as well as individual elements these results are somewhat surprising and contradict the widely held opinion that the continuous galerkin method is not locally conservative

auxiliary space preconditioning for mixed finite element discretizations of richards equation abstract we propose an auxiliary space method for the solution of the indefinite problem arising from mixed method finite element discretizations of scalar elliptic problems the proposed technique uses conforming elements as an auxiliary space and utilizes special interpolation operators for the transfer of residuals and corrections between the spaces we show that the corresponding method provides optimal solver for the indefinite problem by only solving symmetric and positive definite auxiliary problems we apply this preconditioner to the mixed form discretization of richards equation linearized with the l scheme we provide numerical tests validating the theoretical estimates

locally conservative galerkin and finite volume methods for two phase flow in porous media in this paper we propose a locally conservative galerkin lcg finite element method for two phase flow simulations in heterogeneous porous media the main idea of the method is to use the property of local conservation at steady state conditions in order to define a numerical flux at element boundaries it provides a way to apply standard galerkin finite element method in two phase flow simulations in porous media the lcg method has all the advantages of the standard finite element method while explicitly conserving fluxes over each element all the examples presented show that the formulation employed is accurate and robust while using less cpu time than finite volume method

on convergence of finite volume schemes for one dimensional two phase flow in porous media this paper deals with development and analysis of finite volume schemes for a one dimensional nonlinear degenerate convection diffusion equation having application in petroleum reservoir and groundwater aquifer simulation the main difficulty is that the solution typically lacks regularity due to the degenerate nonlinear diffusion term we analyze and compare three families of numerical schemes corresponding to explicit semi implicit and implicit discretization of the diffusion term and a godunov scheme for the advection term l stability under appropriate cfl conditions and bv estimates are obtained it is shown that the schemes satisfy a discrete maximum principle then we prove convergence of the approximate solution to the weak solution of the problem results of numerical experiments using the present approach are reported

new two dimensional slope limiters for discontinuous galerkin methods on arbitrary meshes summary in this paper we introduce an extension of van leer s slope limiter for two dimensional discontinuous galerkin dg methods on arbitrary unstructured quadrangular or triangular grids the aim is to construct a non oscillatory shock capturing dg method for the approximation of hyperbolic conservative laws without adding excessive numerical dispersion unlike some splitting techniques that are limited to linear approximations on rectangular grids in this work the solution is approximated by means of piecewise quadratic functions the main idea of this new reconstructing and limiting technique follows a well known approach where local maximum principle regions are defined by enforcing some constraints on the reconstruction of the solution numerical comparisons with some existing slope limiters on structured as well as on unstructured meshes show a superior accuracy of our proposed slope limiters copyright 2004 john wiley sons ltd

construction of locally conservative fluxes for high order continuous galerkin finite element methods abstract despite their robustness it is known that standard continuous galerkin finite element methods cgfems do not produce a locally conservative flux field as a result their application to solving model problems that are derived from conservation laws can be limited to remedy this issue some form of post processing must be performed on the cgfem solution in this work a simple post processing technique is proposed to obtain a locally conservative flux field from a cgfem solution one distinct advantage of the proposed method is that it produces continuous normal flux at the element s boundary the post processing is implemented on nodal centered control volumes that are constructed from the original finite element mesh the post processing method is performed by solving an independent set of low dimensional problems posed on each element the associated linear algebra systems are of dimension 1 2 k 1 k 2 where k is the polynomial degree of cgfem basis on a triangular mesh a theoretical investigation is conducted to confirm that the post processed solution converges in an optimal fashion to the true solution in the h 1 semi norm various numerical examples that demonstrate the performance of technique are given specifically a simulation of a model for single phase flow in a heterogeneous system is presented to show the necessity of the local conservation as well as the effective performance of the post processing technique

least squares mixed finite element solution of variably saturated subsurface flow problems a least squares mixed finite element formulation is applied to the nonlinear elliptic problems arising in each time step of an implicit euler discretization for variably saturated flow problems this approach simultaneously constructs approximations to the flux in raviart thomas spaces and to the hydraulic potential by standard h1 conforming linear finite elements two important properties of the least squares approach are investigated in detail the local least squares functional provides an a posteriori error estimator and gauss newton methods are robust iterative solvers for the resulting nonlinear least squares problems computational experiments conducted for a realistic water table recharge problem illustrate the effectiveness of this approach

a weighted difference scheme and monotone iterative methods for quasilinear boundary value problems abstract we consider the boundary value problem y xx f x y y x g x y 0 0 x y 0 b 0 y 1 b 1 we present a weighted two sided difference scheme to approximate the differential equation monotone iterative methods are proposed to solve the resulting nonlinear system the scheme applies equally well to multidimensional analogues numerical results are included

locally conservative stabilized finite element methods for variably saturated flow standard galerkin finite element methods for variably saturated groundwater flow have several deficiencies for instance local oscillations can appear around sharp infiltration fronts without the use of mass lumping and velocity fields obtained from differentiation of pressure fields are discontinuous at element boundaries here we consider conforming finite element discretizations based on a multiscale formulation along with recently developed local postprocessing schemes the resulting approach maintains the basic flexibility and appeal of traditional finite element methods while controlling nonphysical oscillations and producing element wise mass conservative velocity fields accuracy and efficiency of the proposed schemes are evaluated through a series of steady state and transient variably saturated groundwater flow problems in homogeneous as well as heterogeneous domains the schemes are formulated for a generic nonlinear advection diffusion equation and are thus applicable to many other flow models

a runge kutta discontinuous galerkin method for viscous flow equations this paper presents a runge kutta discontinuous galerkin rkdg method for viscous flow computation the construction of the rkdg method is based on a gas kinetic formulation which not only couples the convective and dissipative terms together but also includes both discontinuous and continuous representation in the flux evaluation at a cell interface through a simple hybrid gas distribution function due to the intrinsic connection between the gas kinetic bgk model and the navier stokes equations the navier stokes flux is automatically obtained by the present method numerical examples for both one dimensional 1d and two dimensional 2d compressible viscous flows are presented to demonstrate the accuracy and shock capturing capability of the current rkdg method

novel semi implicit locally conservative galerkin silcg methods application to blood flow in a systemic circulation abstract three novel locally conservative galerkin lcg methods in their semi implicit form are proposed for 1d blood flow modelling in arterial networks these semi implicit discretisations are the second order taylor expansion silcg te method the streamline upwind petrov galerkin silcg supg procedure and the forward in time and central in space silcg ftcs method in the lcg method enforcement of the flux continuity condition at the element interfaces allows to solve the discretised system of equations at element level for problems with a large number of degrees of freedoms this offers a significant advantage over the standard continuous galerkin cg procedure the well established fully explicit lcg method is used for assessing the accuracy of the proposed new methods results presented in this work demonstrate that the proposed silcg methods are stable and as accurate as the explicit lcg method among the three methods proposed the silcg ftcs method requires considerably lower number of iterations per element and thus requires lowest amount of cpu time on the other hand the silcg te and silcg supg methods are stable and accurate for larger time step sizes although the standard newton method requires evaluation of both the jacobian matrix and the residual for every single iteration which may be expensive for standard implicit solvers the computed results show that the maximum number of iterations per element for silcg te and silcg supg is less than unity less than 0 3 and 0 7 respectively also numerical experiments show that the jacobian matrix can be calculated only once per time step allowing to save a significant amount of computational time

a space time discontinuous galerkin method for linearized elastodynamics with element wise momentum balance abstract we present a new space time discontinuous galerkin finite element method for linearized elastodynamics that delivers exact balance of linear and angular momentum over every space time element the method is formulated for use with fully unstructured space time grids and uses displacement basis functions that are discontinuous across all inter element boundaries we introduce a new space time formulation of continuum elastodynamics that uses differential forms and the exterior calculus on manifolds to generate a system of space time field equations and jump conditions then we invoke a bubnov galerkin weighted residuals procedure to formulate the finite element method we describe an implementation on patch wise causal meshes that features linear complexity in the number of elements and special per pixel accurate visualization numerical examples confirm an a priori error estimate and demonstrate the method s shock capturing capabilities

nilpotence of a class of commutative power associative nilalgebras abstract let a be a commutative algebra over a field f of characteristic 2 3 in m gerstenhaber on nilalgebras and linear varieties of nilpotent matrices ii duke math j 27 1960 21 31 m gerstenhaber proved that if a is a nilalgebra of bounded index t and the characteristic of f is zero or greater than 2 t 3 then the right multiplication r x is nilpotent and r x 2 t 3 0 for all x a in this work we prove that this result is also valid for commutative power associative algebras of characteristic t in section 3 we prove that when a is a power associative nilalgebra of dimension 6 then a is nilpotent or a 2 2 0 in section 4 we prove that every power associative nilalgebra a of dimension n and nilindex t n 1 is either nilpotent of index t or isomorphic to the suttles example

on the continuum scale modeling of gravity driven fingers in unsaturated porous media the inadequacy of the richards equation with standard monotonic constitutive relations and hysteretic equations of state we consider the ability of the continuum scale richards equation re with standard monotonic constitutive relations and hysteretic equations of state to model gravity driven fingers in unsaturated porous media and in particular the underlying nonmonotonicity observed along the vertical extent of fingers as published in a number of recent papers finger like solutions with nonmonotonic profiles can be simulated numerically using a downwind averaging method however we find these fingers to be artifacts generated by the combined effects of a truncation error induced oscillation or oversaturation at the wetting front and capillary hysteresis as the oscillation is removed either through grid refinement or the use of inherently monotone schemes the numerically generated fingers disappear and the solution becomes monotonic thus the re along with standard monotonic hydraulic properties does not contain the critical physics required to model gravity driven fingers and must be considered inadequate for unsaturated flow in initially dry highly nonlinear and hysteretic media where these fingers occur

discontinuous galerkin bgk method for viscous flow equations one dimensional systems this paper is about the construction of a bgk navier stokes bgk ns solver in the discontinuous galerkin dg framework since in the dg formulation the conservative variables and their slopes can be updated simultaneously the flow evolution in each element involves only the flow variables in the nearest neighboring cells instead of using the semidiscrete approach in the runge kutta discontinuous galerkin rkdg method the current dg bgk method integrates the governing equations in time as well due to the coupling of advection and dissipative terms in the gas kinetic formulation the dg bgk method solves the viscous governing equations directly numerical examples for the one dimensional compressible navier stokes solutions will be presented

a finite element method for the 1 d water flooding problem with gravity abstract the numerical simulation of the one dimensional displacement of oil by water in a vertical porous slab is studied the water saturation is governed by a quasilinear diffusion convection equation the diffusion term vanishes for the extreme values of the saturation the transport term may be nonmonotone for small or zero water injection rates in presence of gravity various boundary conditions are used a generalized dirichlet condition for the pure transport case and a condition taking into account the so called well effect on the production boundary for the case with capillary diffusion the above problem is solved using discontinuous finite elements together with mixed finite elements following the ideas of lesaint raviart and thomas godunov s generalization of upstream weighting is also incorporated a computer code of this algorithm works satisfactorily under a wide range of experimental conditions going from the pure diffusion case 0 to the pure transport case 0 results of various runs on idealized data as well as on laboratory data are shown

a multi dimensional high order dg ale method based on gas kinetic theory with application to oscillating bodies this paper presents a multi dimensional high order discontinuous galerkin dg method in an arbitrary lagrangian eulerian ale formulation to simulate flows over variable domains with moving and deforming meshes it is an extension of the gas kinetic dg method proposed by the authors for static domains x ren et al 2015 22 a moving mesh gas kinetic dg method is proposed for both inviscid and viscous flow computations a flux integration method across a translating and deforming cell interface has been constructed differently from the previous ale type gas kinetic method with piecewise constant mesh velocity at each cell interface within each time step the mesh velocity variation inside a cell and the mesh moving and rotating at a cell interface have been accounted for in the finite element framework as a result the current scheme is applicable for any kind of mesh movement such as translation rotation and deformation the accuracy and robustness of the scheme have been improved significantly in the oscillating airfoil calculations all computations are conducted in a physical domain rather than in a reference domain and the basis functions move with the grid movement therefore the numerical scheme can preserve the uniform flow automatically and satisfy the geometric conservation law gcl the numerical accuracy can be maintained even for a largely moving and deforming mesh several test cases are presented to demonstrate the performance of the gas kinetic dg ale method

nilpotent linear transformations and the solvability of power associative nilalgebras abstract we prove some results about nilpotent linear transformations as an application we solve some cases of albert s problem on the solvability of nilalgebras more precisely we prove the following results commutative power associative nilalgebras of dimension n and nilindex n 1 or n 2 are solvable commutative power associative nilalgebras of dimension 7 are solvable

the mast edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media a novel methodology is proposed for the solution of the flow equation in a variably saturated heterogeneous porous medium the computational domain is descretized using triangular meshes and the governing pdes are discretized using a lumped in the edge centres numerical technique the dependent unknown variable of the problem is the piezometric head a fractional time step methodology is applied for the solution of the original system solving consecutively a prediction and a correction problem a scalar potential of the flow field exists and in the prediction step a marching in space and time mast formulation is applied for the sequential solution of the ordinary differential equation of the cells ordered according to their potential value computed at the beginning of the time step in the correction step the solution of a large linear system with order equal to the number of edges is required a semi analytical procedure is also proposed for the solution of the prediction step the computational performance the order of convergence and the mass balance error have been estimated in several tests and compared with the results of other literature models

nilpotency of commutative finitely generated algebras satisfying lx3 γlx3 0 γ 1 0 abstract this paper deals with two varieties of commutative non associative algebras one variety satisfies l x 3 l x 3 0 the other variety satisfies l x 3 0 we prove that in either variety any finitely generated algebra is nilpotent our results require characteristic 2 3

implicit hybrid upwind scheme for coupled multiphase flow and transport with buoyancy abstract numerical simulation of coupled multiphase flow and transport in porous media is used in many scientific and industrial applications such as groundwater management and oil recovery to solve the governing partial differential equations we focus on the fully implicit backward euler finite volume method fim in this numerical scheme large algebraic systems must be solved at each time step using newton s method this can be quite expensive especially for highly nonlinear problems with buoyancy in this work we present a new first order approximation of the flux in the fim leading to improved nonlinear convergence rate and radius this approximation is based on implicit hybrid upwinding and relies on separate treatments of the viscous and buoyancy parts of the numerical flux moreover in the viscous part the total velocity discretization is key as it controls the coupling between the elliptic flow problem and the hyperbolic multiphase transport problem to achieve robustness and efficiency we propose a differentiable total velocity discretization that adapts to the balance of forces at each interface we analyze the theoretical properties of the resulting numerical scheme and prove that saturations remain between physical bounds challenging two and three phase test cases illustrate that our numerical scheme brings a significant reduction in the number of nonlinear iterations compared to a finite volume discretization relying on the widely used phase per phase upstream weighting our numerical scheme therefore reduces the simulation cost while providing similar accuracy

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

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100