The influence of differencing and CFL number on implicit time-dependent non-linear calculations
Copyright policy )The influence of differencing and CFL number on implicit time-dependent non-linear calculations
Analysis of the stability and precision of transient implicit finite difference algorithms is presented on the base of the linearized block implicit method of \textit{H. McDonald} and \textit{W. R. Briley} [ibid. 24, 372-397 (1977; Zbl 0363.76018) and 34, 54-73 (1980; Zbl 0436.76021)]. The test problem is the Burgers equation under various initial conditions. Linear analysis provides incomplete stability conditions for both continuous and weak solutions and a simple criterion of augmented stability taking into account the nonlinearity of the problem is derived.
- École Centrale Paris France
- CentraleSupélec France
Partial differential equations of mathematical physics and other areas of application, implicit finite difference algorithms, stability, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Euler equations, CFL number, block implicit method, First-order nonlinear hyperbolic equations, Burgers equation
Partial differential equations of mathematical physics and other areas of application, implicit finite difference algorithms, stability, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Euler equations, CFL number, block implicit method, First-order nonlinear hyperbolic equations, Burgers equation
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