Showing papers on "MUSCL scheme published in 1999"

On an Approximate Godunov Scheme

Abstract: We are interested in the numerical resolution of hyperbolic systems of conservation laws which do not allow any analytical calculation and for which it is difficult to use classical schemes such as Roe's scheme. We introduce a new finite volume scheme called VFRoe. As the Roe scheme, it is based on the local resolution of a linearized Riemann problem. The numerical flux is defined following the Godunov scheme, as the physical flux evaluated at the interface value of the linearized solver. The VFRoe scheme is conservative and consistent without fulfilling any Roe's type condition. Some numerical tests on shock tube problems and two-phase flows problems are presented.

A Higher-Order Godunov Scheme for Non-Ideal Magnetohydrodynamics

Abstract: We propose a new Godunov-type numerical scheme for magnetohydrodynamics including the effect of ohmic dissipation. Several investigators have worked on the development of accurate numerical methods for magnetohydrodynamics (MHD). Among them, Godunov-type schemes are considered to be efficient for many astrophysical problems where flows are super-sonic. Brio & Wu (1988) and Hanawa et al. (1994) have applied Roe’s method to MHD equations. Zachary & Colella (1992) and Dai & Woodward (1994) have extended PPM to MHD. Although their methods are successful in shock tube problems with moderate shock strength, neither of their methods maintains the divergence-free ( ∇ • B = 0) character of magnetic fields.

A conservative box-scheme for the Euler equations

Abstract: The work presented in this paper shows that the mixed-type scheme of Murman and Cole, originally developed for a scalar equation, can be extended to systems of conservation laws. A characteristic scheme for the equations of gas dynamics is introduced that has a close connection to a four operator scheme for the Burgers-Hopf equation. The results indicate that the scheme performs well on the classical test cases. The scheme has no tuning parameters and can be interpreted as the projection of an L∞-stable scheme. At steady state second order accuracy is obtained as a by-product of the box-scheme feature

A Comparison of Third and Second Order Accurate Finite Volume Schemes for the Two-dimensional Compressible Euler Equations

Abstract: We develop, implement and test a new third order accurate MUSCL type finite volume scheme for the two-dimensional Euler equations of compressible fluid flow and compare the scheme with an analogous second order scheme. It turns out that for many applications the third order scheme is less efficient than the second order one.

Influence of the discretization scheme on the parallel efficiency of a code for the modelling of a utility boiler

Abstract: A code for the simulation of the turbulent reactive flow with heat transfer in a utility boiler has been parallelized using MPI. This paper reports a comparison of the parallel efficiency of the code using the hybrid central differences/upwind and the MUSCL schemes for the discretization of the convective terms of the governing equations. The results were obtained using a Cray T3D and a number of processors in the range 1 - 128. It is shown that higher efficiencies are obtained using the MUSCL scheme and that the least efficient tasks are the solution of the pressure correction equation and the radiative heat transfer calculation.

Fast computation of stationary inviscid flow around an airfoil

Abstract: The parallel performance of an implicit solver for the Euler equations on a structured grid is discussed. The flow studied is a two-dimensional transonic flow around an airfoil. The spatial discretization involves the MUSCL scheme, a higher-order Total Variation Diminishing scheme. The solver described in this paper is an implicit solver that is based on quasi Newton iteration and approximate factorization to solve the linear system of equations resulting from the Euler Backward scheme. It is shown that the implicit time-stepping method can be used as a smoother to obtain an efficient and stable multigrid process. Also, the solver has good properties for parallelization comparable with explicit time-stepping schemes. To preserve data locality domain decomposition is applied to obtain a parallelizable code. Although the domain decomposition slightly affects the efficiency of the approximate factorization method with respect to the number of time steps required to attain the stationary solution, the results show that this hardly affects the performance for practical purposes. The accuracy with which the linear system of equations is solved is found to be an important parameter. Because the method is equally applicable for the Navier-Stokes equations and in three-dimensions, the presented combination of efficient parallel execution and implicit time-integration provides an interesting perspective for time-dependent problems in computational fluid dynamics.

A Second Order Accurate Numerical Scheme for MHD Equations

Abstract: We present a second order accurate numerical scheme for ideal magnetohydrodynamical equations. Our numerical scheme is an upwind scheme based on the flux vector splitting and an extension of Roe’s scheme. The second order accuracy is achieved by MUSCL, the Monotone Upstreamcentered Scheme for Conservation Laws approach. Our numerical scheme ensures the total variation diminishing (TVD) as far as Courant number is smaller than unity.

Computation of Flowfield About Submarine Rocket Using a High Order Godunov Scheme

Abstract: In this paper, a Monotone Upstream-Centered Scheme for Conservation Laws(MUSCL) has been employed to solve two dimensional Navier-Stokes equations. Moving boundaries concerned with rocket walls can be considered. A number of simulated results of submarine rocket launch box are obtained and analyzed. Comparing with available test data show excellent agreement.