An explicit thirdorder algorithm with Courant number three
Abstract
The numerical stability of explicit finitedifference schemes for unsteady flow problems is investigated analytically. It is conjectured that a strictly onesided pthorder scheme based on the lambda approach is stable up to Courant number p, and a proof is presented for p = 3. The algorithm is developed using the MACSYMA algebra compiler and a RungeKutta scheme for the required Taylor expansions, and its performance is documented in test computations on Ringleb flow, using the methods described by Foerster (1978 and 1981). The accuracy of the new algorithm is shown to be about 10 times better than that of the CIA algorithm of Moretti and Zannetti (1982).
 Publication:

Gesellschaft angewandte Mathematik und Mechanik Jahrestagung Goettingen West Germany Zeitschrift Flugwissenschaften
 Pub Date:
 1988
 Bibcode:
 1988GMMWJ..68..298F
 Keywords:

 Computational Fluid Dynamics;
 Finite Difference Theory;
 Numerical Integration;
 Unsteady Flow;
 Computational Grids;
 Error Analysis;
 Fourier Analysis;
 Numerical Stability;
 Fluid Mechanics and Heat Transfer