Abstract
The paper presents a new high-resolution hybrid scheme combining implicit flux vector splitting with Harten's TVD, which is proved suitable for shock-capturing calculation in gasdynamics. Fluxsplitting procedures are applied to discretize the implicit part of the Euler equations whereas Harten's numerical fluxes are used to calculate the residual of steady-state solutions. It ensures good shock-capturing properties and produces sharp numerical discontinuities without oscillations. It excludes expansion shocks and leads only to physically relevant solutions. The block-line-Gauss-Seidel relaxation procedure (block-LGS) is used to solve the resulting difference equations. The time step and the CFL number are much larger than those in the linearized block-alternating-direction-implicit approximate factorization method (block-ADI).
Numerical experiments suggest that the hybrid scheme not only has a fairly rapid convergence rate, but also can generate a highly resolved approximation to the steady-state solution. Hence scheme seems to lead to an effective nonoscillatory shock capturing method for steady transonic flow.
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Project Supported by National Natural Science Foundation of China
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Baoguo, W., Naixing, C. A new, high-resolution shock-capturing hybrid scheme of flux vector splitting-Harten's TVD. Acta Mech Sinica 6, 204–213 (1990). https://doi.org/10.1007/BF02487641
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DOI: https://doi.org/10.1007/BF02487641