A finite element first-order equation formulation for the small-disturbance transonic flow problem

Abstract

The nonlinear, mixed elliptic hyperbolic equation describing a steady transonic flow is considered. The original equation is replaced by a system of first-order equations that are hyperbolic in time and defined in terms of velocity components. Parabolic regularization terms are added to capture shock wave solutions and to damp iterative solution algorithms. A finite element Galerkin method in space and a Crank-Nicolson finite difference method in iterative time are used to reduce the problem to the solution of a system of algebraic equations. Stability and convergence characteristics of the iterative method are discussed. The numerical implementation of the method is explained, and numerical results are presented.