Adaptive methods on unstructured grids for Euler and Navier-Stokes equations

Abstract

Adaptive methods on unsaturated, triangulated grids are considered for solution of the 2-D Euler and Navier-Stokes equations of compressible fluids. The finite-volume method is used for conservative discretization. The equations are approximated by central or upwind discretizations and solved with an explicit Runge-Kutta scheme. Different generation techniques are considered for the construction of suitable initial meshes. The main focus is on the study of adaptive grid methods. corresponding to the local requirements of inviscid and viscous solutions. Central grid refinement and adaptive cell-orientation have been shown to be well-suited for computation of inviscid flows. More sophisticated adaptation concepts are necessary for solution of the Navier-Stokes equations, due to the different scale lengths in viscous flows. For such solutions a method based on virtual stretching is presented, which enables anisotropic grid according to the resolution requirements of different criteria. The capability of these methods is demonstrated by a number of computed flow results.