Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

Tel Aviv University, Tel Aviv, Israel
Journal of Computational Physics (Impact Factor: 2.49). 03/1985; DOI: 10.1016/0021-9991(85)90183-4
Source: NTRS

ABSTRACT The novel implicit and unconditionally stable, high resolution Total Variation Diminishing (TVD) scheme whose application to steady state calculations is presently examined is a member of a one-parameter family of implicit, second-order accurate systems developed by Harten (1983) for the computation of weak solutions for one-dimensional hyperbolic conservation laws. The scheme will not generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments for a quasi-one-dimensional nozzle problem show that the experimentally determined stability limit correlates exactly with the theoretical stability limit for the nonlinear scalar hyberbolic conservation laws.

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