45th AIAA Aerospace Sciences Meeting and Exhibit · 2007 · 43 citations · 20 references
Natural SciencesComputational EngineeringPhysicsComputational Fluid DynamicsComputational MechanicsComputational PhysicsFinite Difference MethodsNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsCompact Finite Difference SchemesFinite Difference DiscretizationFinite Difference SchemesHigh-order Numerical SchemesHigh-order Schemes
The coefficients of higher order weighted compact nonlinear scheme (WCNS) and the resolutions of the family of higher order WCNS are investigated. The coefficients of seventh and ninth order WCNS are calculated by using MATHEMATICA. Seventh and ninth WCNS can resolve the discontinuity without numerical oscillations as well as fifth order WCNS. Seventh and Ninth order WCNS have the higher resolution on the one-dimensional shock-entropy interaction problem with few grid points than fifth order WCNS. In addition, the resolutions of the explicit and tri-diagonal and penta-diagonal compact cell-center to cell-node difference schemes are investigated. The resolutions of these schemes are almost same. Thus the explicit scheme which is cheapest one is good for WCNS. In addition, seventh WCNS can solve the two-dimensional problem with the improvement of resolution, while ninth order can not solve it.
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