**Journal of Theoretical**

and Applied Mechanics

and Applied Mechanics

**35**, 2, pp. 249-261, Warsaw 1997

### Parallel h-adaptive simulations of inviscid flows by the finite element method

The construction and performance of a parallel algorithm for solving the Euler equations on unstructured grids with dynamically distributed data is presented. The algorithm uses a linear, implicit version of the well known Taylor-Galerkin time marching scheme for time discretization. Finite elements are employed for space discretization of one-step problems and an overlapping domain decomposition algorithm combined with the preconditioned GMRES method is used to solve iteratively in parallel the resulting system of linear equations. A new mesh partition algorithm based on the idea of advancing front is described and tested in practice.

The domain decomposition and the mesh partition methods are combined to form a simple and effective algorithm ensuring the optimal load balance for a multiprocessor system.

A general M1MD multiprocessor (multicomputer) system with distributed memory is assumed as the hardware setting for simulations and Parallel Virtual Machine package is used for message passing. The performance of the method is monitored for a well known transient benchmark problem of 2D inviscid flow simulations – the ramp problem.

The domain decomposition and the mesh partition methods are combined to form a simple and effective algorithm ensuring the optimal load balance for a multiprocessor system.

A general M1MD multiprocessor (multicomputer) system with distributed memory is assumed as the hardware setting for simulations and Parallel Virtual Machine package is used for message passing. The performance of the method is monitored for a well known transient benchmark problem of 2D inviscid flow simulations – the ramp problem.

*Keywords*: parallel computations; finite element method; compressible fluid flow