A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier-Stokes equations

作者：Gao X^*; Owen L D; Guzik S M J

来源：International Journal for Numerical Methods in Fluids, 2016, 82(10): 664-688.

DOI：10.1002/fld.4235

• generalized curvilinear coordinate transformation
• fourth-order finite-volume method
• compressible Navier-Stokes algorithm
• mapped grids
• finite-volume Method on mapped grids
• adaptive mesh refinement for mapped grids

A fourth-order finite-volume method for solving the Navier-Stokes equations on a mapped grid with adaptive mesh refinement is proposed, implemented, and demonstrated for the prediction of unsteady compressible viscous flows. The method employs fourth-order quadrature rules for evaluating face-averaged fluxes. Our approach is freestream preserving, guaranteed by the way of computing the averages of the metric terms on the faces of cells. The standard Runge-Kutta marching method is used for time discretization. Solutions of a smooth flow are obtained in order to verify that the method is formally fourth-order accurate when applying the nonlinear viscous operators on mapped grids. Solutions of a shock tube problem are obtained to demonstrate the effectiveness of adaptive mesh refinement in resolving discontinuities. A Mach reflection problem is solved to demonstrate the mapped algorithm on a non-rectangular physical domain. The simulation is compared against experimental results. Future work will consider mapped multiblock grids for practical engineering geometries.

• 出版日期2016-12-10