Test of the accuracy of implicit methods for mechanics of compressible fluids
Abstract
Implicit numerical methods for the solution of the equations of hydrodynamics are tested for their accuracy in a shockwave calculation. A generalized Crank Nicholson Method is used, in which spacederivatives are approximated by a weighted average of space differences at 'old' and 'new' times. Best results are obtained when the 'new' space differences are given a weight of 0.7. Momentum flux is approximated using a nonlinear method (ZIP differencing) which has advantages in symmetry and accuracy over other methods. Results indicate that implicit methods can be used for problems on both short and long time scales.
 Publication:

In: International Symposium on Discrete Methods in Engineering
 Pub Date:
 1974
 Bibcode:
 1974dme..symp..448M
 Keywords:

 Compressible Fluids;
 Error Analysis;
 Finite Difference Theory;
 Hydrodynamic Equations;
 Mathematical Models;
 Shock Wave Propagation;
 Boundary Layer Flow;
 Computer Programs;
 Conservation Equations;
 Continuity Equation;
 Fluid Mechanics;
 Momentum Transfer;
 Power Plants;
 Fluid Mechanics and Heat Transfer