Accuracy of Multiply-Upstream, Semi-Lagrangian Advective Schemes

Abstract

The stability and accuracy of the multiply-upstream, semi-Lagrangian method of integrating the advective equation in two dimensions is examined for four different interpolation schemes; namely, bilinear, biquadratic, bicubic and biquartic. All are shown to be consistent and unconditionally stable for constant advecting velocity. Their respective amplitude and phase errors are discussed. They are then used to integrate the test problem of a cone being advected about the plane at constant angular velocity. The merits of the schemes relative to each other and relative to a well tried Eulerian scheme am examined with particular regard to accuracy and computation time.