Abstract
AbstractThe validity of the equivalent differential equation (also called modified equation or differential approximation) for representing shock solutions of high order schemes is investigated through a comparison of exact analytical solutions of the discrete scheme and its equivalent equation, for steady shocks of the inviscid Bürgers equation. For a third-order dissipative compact scheme, it is shown that the equivalent equation is a very good model of the scheme provided the dispersive term of fourth order is taken into account in addition to the dissipative term of third order.KeywordsMesh PointConservative VariableCell FaceNumerical FluxEquivalent EquationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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