A nonstationary relaxation technique for solving the equations of gas dynamics

A nonstationary relaxation technique specially designed for solving the steady-state equations of gas dynamics is investigated. The approach adopts a form of Newton's method for the solution process. All the nonlinear terms are linearized based on a reference state function which is a assumed state of the dependent variables. Each linear system based about that reference state functions is cast into finite difference form by using central differencing and Dirichlet boundary conditions over the entire mesh. The resulting difference equations solved by a fast nonstationary relaxation scheme. The process is repeated until a convergent criterion is satisfied. Results differencing method when properly interpreted and applied is an efficient way to find time-invariant solutions to the Cauchy-Riemann and Euler equations.