Study for Stability of Finite Difference Solution and its Modified Equation. 2nd Report: for Two Fluid Model Equations.:2nd Report: for Two Fluid Model Equations

概要

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The aim of this papar is to show the mechanism of instability of the Finite Difference Equation (FDE) for a linearized system of Two Fluid Model (TFM) equations by means of the eigenvalues of the coefficient matrix in the modified equation. First, the modified equations of FDE are introduced from the FDE which was obtained by discretizing the linearized system using the two step Lax-Wendroff scheme. Then, we make sure from the modified equations that the instability of the FDE is caused by ill-posedness of original TFM equation system. Furthermore, von Neumann's stability discriminant equation is concretely and analytically expressed by the sum of damping term and growing term, which consist of numerical diffusion from its lowest even order derivative term of the modified equation, and complex eigenvalue due to ill-posedness of the system, respectively. Finally, the influence of these two terms on the stability is directly shown for the various spatial grid sizes.
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