Publications Details
Nonlinear generalized functions and nonconservative shock simulations
This SAND report summarizes the work completed for a Novel Project Research and Development LDRD project. In this research effort, new mathematical techniques from the theory of nonlinear generalized functions were applied to compute solutions of nonlinear hyperbolic field equations in nonconservative form. Nonconservative field equations contain products of generalized functions which are not defined in classical mathematics. Because of these products, traditional computational schemes are very difficult to apply and can produce erroneous numerical results. In the present work, existing first-order computational schemes based on results from the theory of nonlinear generalized functions were applied to simulate numerically two model problems cast in nonconservative form. From the results of these computational experiments, a higher-order Godunov scheme based on the piecewise parabolic method was proposed and tested. The numerical results obtained for the model problems are encouraging and suggest that the theory of nonlinear generalized functions provides a powerful tool for studying the complicated behavior of nonlinear hyperbolic field equations.