摘要:

This paper presents an adaptive finite element method for solving scalar hyperbolic transport problems. An equation for the evolution of the error is developed. The Lesaint-Raviart finite element method is used to solve both the transport problem and the error equation. The use of a hierarchical finite element basis on triangles leads to a very efficient error estimation algorithm. The adaptive strategy, based on remeshing, is dmonstrated on several non-trivial problems with known analytical solutions. Higher degree polynomials combined with adaptation produce a very efficient solution algorithm even for problems involving discontinuities.

ISSN:1061-8562    

DOI:10.1080/10618569408904501

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The objectives of this paper are to present the development and implementation of parallel numerical methods for inviscid and viscous compressible flows. A flux vector splitting scheme and a Riemann solver were used to discretize the Euler and Navier-Stokes equations. Furthermore, an implicit unfactored procedure with Gauss-Seidel relaxation was used to solve the equations in time dependent form. Acceleration of the convergence was achieved by the local solution method and the mesh sequencing technique. Grid partitioning was utilized for the parallelization of the methods. Calculations were performed on various parallel platforms and factors that can influence the parallel performance, such as numerical method, acceleration procedure, grid size, and interprocessor communication were investigated.

ISSN:1061-8562    

DOI:10.1080/10618569408904502

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We have analyzed several different approaches for simulating the fluid motion of a stratified two-phase system. The flow regime is transformed to a regular domain for numerical integration and the standard finite difference formulas are applied to discretize the governing and mapping equations. Five different interface iteration schemes that are based on the kinematic condition and the normal stress balance have been derived to update the position of the liquid-liquid interface. We have found that the iterative scheme based on the normal stress balance is more stable and is applicable to a wide range of capillary numbers, and that these appear to be the only sensitive parameter in the stratified two-phase system under consideration.

ISSN:1061-8562    

DOI:10.1080/10618569408904503

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

A family of spatially third order accurate Compact Upwind Difference schemes is derived for the scalar and vector conservation laws and put in the numerical flux form. A third order flux correction extracted from these schemes is applied to the first order Roe and Osher-Solomon fluxes. A lemma due to Tadmor is then used to limit the high order fluxes of the new schemes so as to render them TVD in the scalar case. Applied to systems, the flux limited versions perform well in limiting the oscillations in the computed solutions.

ISSN:1061-8562    

DOI:10.1080/10618569408904504

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor