Multidimensional FEM‐FCT schemes for arbitrary time stepping
- 13 May 2003
- journal article
- research article
- Published by Wiley in International Journal for Numerical Methods in Fluids
- Vol. 42 (3) , 265-295
Abstract
The flux‐corrected‐transport paradigm is generalized to finite‐element schemes based on arbitrary time stepping. A conservative flux decomposition procedure is proposed for both convective and diffusive terms. Mathematical properties of positivity‐preserving schemes are reviewed. A nonoscillatory low‐order method is constructed by elimination of negative off‐diagonal entries of the discrete transport operator. The linearization of source terms and extension to hyperbolic systems are discussed. Zalesak's multidimensional limiter is employed to switch between linear discretizations of high and low order. A rigorous proof of positivity is provided. The treatment of non‐linearities and iterative solution of linear systems are addressed. The performance of the new algorithm is illustrated by numerical examples for the shock tube problem in one dimension and scalar transport equations in two dimensions. Copyright © 2003 John Wiley & Sons, Ltd.Keywords
This publication has 25 references indexed in Scilit:
- Flux Correction Tools for Finite ElementsJournal of Computational Physics, 2002
- Unstructured grid finite-element methods for fluid mechanicsReports on Progress in Physics, 1998
- Aspects of conservation in finite element flow computationsComputer Methods in Applied Mechanics and Engineering, 1994
- Computational algorithms for aerodynamic analysis and designApplied Numerical Mathematics, 1993
- A New Flux Splitting SchemeJournal of Computational Physics, 1993
- The group finite element formulationComputer Methods in Applied Mechanics and Engineering, 1983
- Approximate Riemann solvers, parameter vectors, and difference schemesJournal of Computational Physics, 1981
- Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methodsJournal of Computational Physics, 1981
- Fully multidimensional flux-corrected transport algorithms for fluidsJournal of Computational Physics, 1979
- Flux-corrected transport. I. SHASTA, a fluid transport algorithm that worksJournal of Computational Physics, 1973