Multioperators Technique for Constructing Arbitrary High-Order Approximations and Schemes: Main Ideas and Applications to Fluid Dynamics Equations
The main ideas of multioperators as tools for constructing arbitrary high-order approximations and schemes are outlined. Examples of multioperators-based numerical analysis formulas are presented. Schemes for fluid dynamics with multioperators approximations up to 36th-order are described. Numerical results of high fidelity long term calculations for instability and sound radiation problems are presented. The extension to strongly discontinuous solutions is briefly outlined.
KeywordsMultioperators Multioperators-based formulas Schemes for fluid dynamics Euler and Navier-Stokes equations Instability and sound radiation Discontinuous solutions
- 1.Tolstykh, A.I.: Multioperator high-order compact upwind methods for CFD parallel calculations. In: Emerson, D., Fox, P., Satofuka, N. (eds.) Parallel Computational Fluid Dynamics: Recent Developments and Advances Using Parallel Computing, Elsevier, pp. 383–390 (1998)Google Scholar
- 4.Tolstykh, A.I.: High accuracy compact and multioperators approximations for partial differential equations. Nauka, Moscow (2015). (in Russian)Google Scholar
- 7.Shu, C.-W.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws: NASA/CR-97-206253, ICASE Rept No. 97-65. Hampton: Langley Res. Center (1997)Google Scholar
- 8.Tam, C.K.W.: Problem 1-aliasing. 4th Computational Aeroacoustics (CAA) Workshop on benchmark problems, NASA/CP-2004–2159 (2004)Google Scholar