1999•Numerical Heat Transfer Part B FundamentalsRequires access

STABILITY ANALYSIS FOR DISCRETIZED STEADY CONVECTIVE-DIFFUSION EQUATION

Wen-Quan Tao Ming-Jiu Ni

Abstract

A comprehensive study is presented regarding the numerical stability of several common iteration numerical methods applied to the discretized steady convective-diffusion equations with some common finite-difference spatial discretizations. One-dimensional and multidimensional results are obtained using the classical Von Neumann method of stability analysis. The analysis results show that numerical stability in solving the resulting discretization equations depends on both the finite-difference scheme and the numerical method for solving the resulting algebraic equations.

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Key concepts: Discretization, Von Neumann stability analysis, Stability (learning theory), Numerical stability, Mathematics, Convection–diffusion equation, Numerical analysis, Finite difference method