Finite volume, adaptive-multigrid methods for Euler and Navier-Stokes equations on three-dimensional unstructured grids

A conservative, 3D finite volume scheme for simulation of inviscid flows using adaptive, unstructured grids is presented. The scheme is node-centered and uses central-differencing type spatial discretization. All operations pertaining to the numerical scheme are cast on an edge-wise basis, making the scheme efficient both in terms of storage and computation. An explicit, time-marching method is used to obtain the steady-state solution of the governing Euler equations. The solver uses a one step, Lax-Wendroff scheme for time-stepping the solution to steady state. The time-accuracy of the solution is not preserved by the local time-stepping scheme. Upwind-like dissipation operators are developed for shock capturing and background smoothing. The artificial dissipation model is developed along the lines of implicit damping terms of the flux-difference splitting scheme of Roe. The finite volume solver is implemented in conjunction with a grid adaptation algorithm that employs different types of tetrahedral cell refinement strategies to increase the resolution of the grid locally in the regions of significant flow variations. The adaptive algorithm is guided by a feature detector to accomplish this task.; A multigrid method for adaptive, tetrahedral grids is developed in order to accelerate the convergence to steady state. The multigrid method employs successively coarser and nested grids that are easily generated when implemented along with the adaptation algorithm, by using the cell-tree structure of an embedded grid. Two different approaches to the multigrid method namely global and zonal methods are presented. The finite volume solver combined with grid adaptation and multigrid acceleration is applied to subsonic, transonic as well as supersonic flows past 3D geometries. Applications include compressible flow past a cylindrical bump in a channel, transonic flow past a ONERA M6 wing and transonic flow past a Low Wing Transport aircraft configurations. The accuracy of the numerical results is validated by comparison with experimental observations. CPU time comparisons are made to show the efficiency of the multigrid scheme in obtaining significant speed-up in obtaining the steady-state solution.; The multigrid method is extended to viscous flow computations on prismatic grids, which are unstructured in the lateral direction and structured in the normal-to-the-surface direction. The integration scheme is similar to that of the Euler solver. The Navier-Stokes solver is used with a prismatic grid adaptation scheme which is equivalent to 2D triangular grid adaptation. The prismatic multigrid scheme is applied to internal as well as external flow problems at both low and high Reynolds number.