DIRECT AND ITERATIVE ALGORITHMS FOR THE 3-DIMENSIONAL EULER EQUATIONS

Direct and iterative algorithms have been developed for solving a fini te volume discretization of the three-dimensional Euler equations in c urvilinear coordinates. The Euler equations are discretized using nume rical derivatives of the numerical flux vector for the Jacobians. Two direct solvers are formulated, one of which has a diagonal plane matri x structure with significantly lower memory requirements. The direct s olvers are used as a benchmark in measuring the convergence rate and r obustness of more computationally efficient solvers which include two factored approaches, a Newton-relaxation algorithm and a discretized N ewton-relaxation algorithm, which uses numerical Jacobians. A diagonal plane formulation for the Newton-relaxation algorithms has also been developed that may have the potential for massive parallelization. It is demonstrated that the Newton-relaxation approach can give convergen ce rates and robustness equal to that of a direct solver for three-dim ensional problems. As a demonstration of the robustness of both the Ne wton-relaxation algorithm and numerical Jacobians, quadratic convergen ce to machine zero is demonstrated.