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An efficient parallel algorithm with application to computational fluid dynamics. (English) Zbl 1035.65096

Summary: When solving time-dependent partial differential equations on parallel computers using the nonoverlapping domain decomposition method, one often needs numerical boundary conditions on the boundaries between subdomains. These numerical boundary conditions can significantly affect the stability and accuracy of the final algorithm.
In this paper, a stability and accuracy analysis of the existing methods for generating numerical boundary conditions will be presented, and a new approach based on explicit predictors and implicit correctors will be used to solve convection-diffusion equations on parallel computers, with application to aerospace engineering for the solution of Euler equations in computational fluid dynamics simulations. Both theoretical analyses and numerical results demonstrate significant improvement in stability and accuracy by using the new approach.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics (general theory)
76M20 Finite difference methods applied to problems in fluid mechanics
35K15 Initial value problems for second-order parabolic equations
65Y05 Parallel numerical computation

Software:

MPI
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Full Text: DOI

References:

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