This paper presents a nonlinear solver based on the Newton-Krylov methods, where the Newton equations are solved by Krylov-subspace type approaches. We focus on the solution of unsteady systems, in which the temporal terms are discretized by the backward Euler method using finite difference. To save computational cost, an adaptive time stepping is used to minimize the number of time steps. The ...

We consider Newton-Krylov methods for solving discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is crucial for the efficiency of the solver. In this paper we consider a point-block Gauss-Seidel method as preconditioner. We describe and compare renumbering strategies that aim at improving the quality of this preconditioner. A variant of reordering meth...

A fully implicit solver is developed for the mesoscale nonhydrostatic simulation of atmospheric flows governed by the compressible Euler equations. To spatially discretize the Euler equations on a height-based terrain-following mesh, we apply a cell-centered finite volume scheme, in which an AUSM-up method with a piecewise linear reconstruction is employed to achieve secondorder accuracy for th...

In this work we present a subdomain partitioning strategy applied to an explicit high-resolution Euler solver. We describe the design of a parallel multi-domain code suitable for distributed memory multi-processors. We present several implementations on a distributed virtual shared memory computer as well as on a network of workstations. We give computational results to illustrate the eeciency ...

The implementation of a 2D Euler solver on graphics hardware is described. The graphics processing unit is highly parallelised and uses a programming model that is well suited to flow computation. Results for a transonic turbine cascade test-case are presented. For large grids (10 nodes) a 40 times speed-up compared to a Fortran implementation on a contemporary CPU is observed.

In this paper we present a C++ implementation of a numerical solver for the Euler equations about rotating geometries (Turbomachinery). This implementation represents a working prototype C++ solver which obtains performances comparable to a reference Fortran application. We obtain this performance by providing abstractions at the level of collections of objects , thus minimizing the introductio...