A New Stability-Guaranteed Second-Order Difference Scheme

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Abstract
Based on the stability-controllable second-order difference (SCSD) scheme, a new stability-guaranteed second-order difference (SGSD) scheme is proposed whose merits are absolutely stable and adaptive. Its numerical accuracy is at least no less than that of the central difference (CD) and second-order upwind difference (SUD) schemes and sometimes higher than that of the QUICK scheme. The SGSD scheme can automatically choose a different difference scheme according to the available local field information in difference space or time. It automatically approaches the central difference scheme where or when diffusion is dominant, and approaches the second-order upwind difference scheme where or when convection is dominant. Computations for two benchmark problems using the SGSD and the other three schemes show its feasibility in engineering computations.