PSEUDOSPECTRAL METHODS WITH OPEN BOUNDARY-CONDITIONS FOR THE STUDY OF ATMOSPHERIC WAVE PHENOMENA

We consider Chebyshev pseudospectral methods for the study of atmospheric wave phenomena. The governing equations are the two-dimensional Euler equations for gas dynamics with gravity included, where accurate numerical approximation of the nonlinear behaviour is important. The methods are efficiently implemented on a Cray X-MP, and run at nearly optimal speed on one processor. In this case, space derivatives are calculated more efficiently with matrix multiplication than by the Fast Fourier Transform. The boundaries are artificial and we simulate open boundaries by using the characteristic variables of the equations. Different choices of such boundary conditions and their effects on the solutions are discussed. Numerical calculation of an example where the solution may be analytically verified is presented, and the pseudospectral method is seen to be well suited for these computations. © 1990.