A New Theory of Shock Dynamics
Consider a system of conservation laws with given initial or boundary conditions such that the solution contains a single shock surface whose initial position and shape is known. Shock dynamics is a mathematical theory to calculate successive positions and geometry of the shock surface without resort to finding the solution behind the shock. Such a theory based on intuitive arguments, was provided by Whitham (1957, 1959).The only justification of this theory came from the agreement of its results with those obtained from experiments and some purely numerical methods. However, it has only recently been shown by Prasad (1990); and Prasad Ravindran and Sau (1991) that Whitham’s shock dynamics cannot be theoretically justified and can give completely wrong results. We present here a new theory of shock dynamics by Ravindran and Prasad (1990) which is based on exact mathematical results on the compatibility conditions on the shock manifold.
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