A free Lagrange method for gas dynamics

Abstract

This paper presents a new Lagrangian approach to the numeric solution of the equations of gas dynamics in two dimensions. This new method, the signal method, is implemented here as a free Lagrange method using the code FLAME. The signal method is conservative, stable, unsplit, positive definite, accurately tracks strong shock fronts with ease, and adapts to and follows complex gas flows for long times. No artificial viscosities are introduced. The implementation is first-order, but produces results comparable to modern second-order Eulerian techniques, even for problems well-suited to Eulerian computations. For the many other problems where Lagrangian methods are superior a relative advantage is held by the signal method. No special knowledge of the solution is required in advance, and only local information is used.