Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

High-accuracy numerical methods for incompletely parabolic problems in fluid dynamics I:formulation

Maria Morandi Cecchia,*, Maria A. Pirozzib
aDipartimento di Matematica Pura e Applicata, University of Padova, Italy  bIstituto di Matematica, Fisica e Applicazioni, University of Napoli 'Parthenope', Italy

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We continue to investigate a family of fully discrete finite difference implicit methods already proposed for the numerical solution of multidimensional hyperbolic and convection-diffusion equations. In this paper the extension of the schemes to the resolution of two-dimensional incompletely parabolic problems is considered. The basic idea is to discretize and then to split the resulting system of algebraic equations into a collection of tridiagonal subsystems associated with each gridline. The truncation error analysis leads to conditions on the order of accuracy. The classical Von Neumann method is applied to assess the stability of the schemes which is guaranteed with no restriction on the time step.

Keywords:  Mixed hyperbolic-parabolic systems; Finite-difference; High-order schemes; Splitting methods

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