A Parallel Adaptive Newton-Krylov-Schwarz Method for 3D Compressible Inviscid Flow Simulations

Marzio Sala,Angelo Casagrande,Pénélope Leyland

doi:10.1155/2013/694354

Abstract

A parallel adaptive pseudo transient Newton-Krylov-Schwarz (αΨNKS) method for the solution of compressible flows is presented. Multidimensional upwind residual distribution schemes are used for space discretisation, while an implicit time-marching scheme is employed for the discretisation of the (pseudo)time derivative. The linear system arising from the Newton method applied to the resulting nonlinear system is solved by the means of Krylov iterations with Schwarz-type preconditioners. A scalable and efficient data structure for theαΨNKS procedure is presented. The main computational kernels are considered, and an extensive analysis is reported to compare the Krylov accelerators, the preconditioning techniques. Results, obtained on a distributed memory computer, are presented for 2D and 3D problems of aeronautical interest on unstructured grids.

Highlights

E aim of this paper is to provide an overview of the methods required for an efficient parallel solution of the compressible Euler equations (CEE) on unstructured 2D and 3D grids. e ingredients include space and time discretisation schemes for the underlying partial differential equations (PDEs), a nonlinear solver based on the Newton’s method, and a parallel Krylov accelerator with domain decomposition preconditioners
E framework presented here can be successfully applied to the solution of sets of PDEs problems discretised on unstructured grids. e focus in this paper is restricted to the solution of the CEE
Multidimensional upwind schemes have reached a certain degree of maturity for the solution of the steady-state compressible Euler equations on unstructured grids made up of triangles and tetrahedrons. ey can be used for complex aerodynamic ows, in the subsonic, transonic, and supersonic regime

Summary

Introduction

E aim of this paper is to provide an overview of the methods required for an efficient parallel solution of the compressible Euler equations (CEE) on unstructured 2D and 3D grids. e ingredients include space and time discretisation schemes for the underlying partial differential equations (PDEs), a nonlinear solver based on the Newton’s method, and a parallel Krylov accelerator with domain decomposition preconditioners. E linear system arising from the Newton method applied to the resulting nonlinear system is solved by the means of Krylov iterations with Schwarz-type preconditioners. E aim of this paper is to provide an overview of the methods required for an efficient parallel solution of the compressible Euler equations (CEE) on unstructured 2D and 3D grids.

Results

Conclusion