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We present a Chimera method for the numerical solution of incompressible flows past objects in relative motion. The Chimera method is implemented as an iteration-by-subdomain method based on Dirichlet/Neumann(Robin) coupling. The DD method we propose is not only geometric but also algorithmic, for the solution on each subdomain is obtained on separate processes and the exchange of information between the subdomains is carried out by a master code. This strategy is very flexible as it requires almost no modification to the original numerical code. Therefore, only the master code has to be adapted to the numerical codes and the strategies used on each subdomain. As a basic flow solver, we a use stabilized finite element method. [Copyright &y& Elsevier]

This paper introduces a preconditioned variational multiscale stabilization (P-VMS) method for compressible flows. In this introductory paper we focus on inviscid flow and steady state problems. The Euler equations are solved on fully unstructured grids and discretized using the finite element method. The P-VMS method can be decomposed into three parts. First, a local preconditioner is applied to the continuous equations to reduce the stiffness while covering a wide range of Mach numbers. Then, the resulting preconditioned system is discretized in space using finite elements and stabilized with a variational multiscale stabilization method adapted for the preconditioned equations. In this paper, the solution is advanced in time using a fully explicit time discretization, although P-VMS is general and can be applied to fully implicit solvers. The proposed method is assessed by comparing convergence and accuracy of the solutions between the non-preconditioned and preconditioned cases, in particular for van Leer–Lee–Roe ’s (1991) and Choi-Merkle ’s (1993) preconditioners, in some selected examples covering a large range of Mach numbers. [ABSTRACT FROM AUTHOR]

The results of a Fourier stability analysis of the preconditioned variational multiscale stabilization (P-VMS) method introduced in Moragues et al. (2015) are presented in this paper. P-VMS combines a variational multiscale stabilized finite elements discretization together with local preconditioning. In this work, we deal with the P-VMS method using van Leer–Lee–Roe ’s (vanLeer et al., 1991) and Choi–Merkle ’s (Choi and Merkle, 1993) local preconditioners. We solve the Euler equations of compressible flow for steady problems. We concentrate on explicit time integration schemes. The stability analysis is performed on a two dimensional simplified problem with a structured mesh and its conclusions are applied to two and three dimensional general problems with unstructured meshes. As a result of this analysis a local Courant–Friedrichs–Lewy number is defined for the computation of the time step. The convergence rate is evaluated, and compared with the traditional constant Courant–Friedrichs–Lewy number for various test cases spanning a large range of Mach numbers. [ABSTRACT FROM AUTHOR]