Abstract
Total Variation Diminishing (TVD) schemes are widely used to capture high resolution and non_x0002_oscillatory supersonic and hypersonic flow problems. However, discretization and decoupling of the governing equations into nonlinear wave equation induces false numerical dissipation which affects the accuracy of results as well as rate of convergence. This deficiency of TVD schemes can be reduced by an adequate treatment of various parameters that signifies the effect of this dissipation. An appropriate scaling of eigenvectors and eigenvector matrix is one of the strategies to control the amount of numerical dissipation. In present work, hybrid scaling based on some classical scaling factors is proposed and tested on shock tube problem using SOD, Lax and Inverse Shock test cases. Although the computed results are found to be slightly less dissipative in comparison to the scaling used by Hoffmann and Yee, the proposed hybridized scaling and its theoretical aspects on Harten’s 2nd order TVD scheme has opened new challenges for the researchers.
Keyword(s)
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