Implicit solution strategies for compressible flow equations on unstructured meshes

Doctorat en sciences appliquéesinfo:eu-repo/semantics/nonPublishe

Non-overlapping preconditioners for a parallel implicit Navier-Stokes solver

Parallel implicit iterative solution techniques are considered for application to a compressible hypersonic Navier-Stokes solver on unstructured meshes. The construction of parallel preconditioners with quasi-optimal convergence properties with respect to their serial counterpart is a key issue in the design of modern parallel implicit schemes. Two types of non-overlapping preconditioners are presented and compared. The first one is an additive Schwarz preconditioner requiring overlapping of the mesh and the second one is based on a Schur complement formulation. Both are using incomplete LU factorisation at the subdomain level but scale differently. Results are presented for computations on the Cray T3D under the message passing interface MPI. Copyright © 1998 Elsevier Science B.V.info:eu-repo/semantics/publishe

Solving steady compressible flow problems with subspace iteration methods

suppl. 1info:eu-repo/semantics/publishe

Implicit upwind residual-distribution Euler and Navier-Stokes solver on unstructured meshes

Implicit iterative solution techniques are considered for application to a compressible Euler and Navier-Stokes solver using upwind residual-distribution schemes on unstructured meshes. Numerical evaluation of the complete Jacobian matrix needed for the linearization process is achieved at low cost, either by finite difference approximation or by Broyden's update. It enables nonlinear solution strategies such as Newton iterative methods where linear systems are solved approximately using an accelerated iterative scheme. The linearized backward Euler scheme is used to integrate the discretized equations in time, together with a simple time-step evolution strategy. Alternatively, when this strategy fails, it is possible to use a fixed-point acceleration method that has proven quite robust. Numerical applications show the efficiency of the iterative strategy for various flow conditions.info:eu-repo/semantics/publishe

A parallel, implicit, multi-dimensional upwind, residual distribution method for the Navier-Stokes equations on unstructured grids

A multi-dimensional cell-vertex upwind discretization technique for the Navier-Strokes equations on unstructured grids is presented. The grids are composed of linear triangles in two and linear tetrahedra in three space dimensions. The nonlinear upwind schemes for the inviscid part can be viewed as a multi-dimensional generalization of the Roe-scheme, but also as a special class of Petrov-Galerkin schemes. They share with these schemes a compact Galerkin stencil, and are in addition monotonic by construction. The Petrov-Galerkin interpretation of the discretization technique allows a straightforward extension to the Navier-Strokes equations. For linear elements this boils down to a Galerkin discretization for the viscous terms. Compared to standard finite-volume methods on these grids, the method shows an increased accuracy, which becomes comparable with structured grid algorithms. The spatially discretized set of equations is integrated in time using the Backward Euler time integration method. The full Jacobian matrix is computed, either numerically by finite differences or approximated analytically, and stored. The resulting set of linear equations is solved by a Block MILU(0) preconditioned Krylov subspace method. For this purpose the Aztec library of SANDIA National Laboratories is used, which also takes care of the parallelization process and completely hides the details for the user. Results are presented for a two-dimensional turbulent shock wave boundary layer interaction in a nozzle and the turbulent flow over an ogive cylinder. All computations have been performed on the Cray T3E of the Technical University of Delft.info:eu-repo/semantics/publishe