A Pseudospectral Scheme for the Numerical Calculation of Shocks
Abstract
A pseudospectral numerical scheme is developed in order to calculate the propagation of a shock wave. We use a twostep timedifferencing method and a Chebyshev transform method to compute the space derivative. Such a scheme has been used to reduce the oscillations due to Gibb's phenomenon. This numerical method is applied to the solution of the Burgers equation without viscosity term. The accuracy of the numerical solutions is compared to the one given by two finite difference methods.
 Publication:

Journal of Computational Physics
 Pub Date:
 July 1982
 DOI:
 10.1016/00219991(82)900699
 Bibcode:
 1982JCoPh..47..146C
 Keywords:

 Burger Equation;
 Chebyshev Approximation;
 Gibbs Phenomenon;
 Shock Wave Propagation;
 Fast Fourier Transformations;
 Finite Difference Theory;
 Oscillations;
 Spectrum Analysis;
 Step Functions;
 Fluid Mechanics and Heat Transfer