A variable node finite element method applied to the gas dynamics equations

The author's variable node finite element method has been extended to systems of partial differential equations in one space dimension and applied to the gas dynamics equations in conservation form with a numerical viscosity to smear out the discontinuities. The method for gas dynamics was implemented in the computer program VFEGD and tested successfully on a shock tube problem. Since the variable node method concentrates nodes in regions of large gradients, it makes possible automatic numerical detection of contact discontinuities and shocks. Once they have been detected, they can be sharpened and consequently their diffusion can be controlled. The program VFEGD, with modifications to detect and sharpen contacts and shocks, was also tested successfully on the shock tube problem. (Author).