SEMI-LAGRANGIAN ADVECTIVE SCHEMES AND THEIR NONLINEAR COMPUTATIONAL CHAOS*

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* Supported by National Natural Science Foundation of China.

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  • Abstract

    In this paper,we have suggested several interpolating formulae which are convinient for vector computers to perform vector calculation.Analysis shows that for a simple advective problem,the semi-Lagrangian schemes constructed with these formulae are linearly unconditionally stable.Moreover,we have discussed the nonlinear computational chaos in the semi-Lagrangian schemes.It is found that for a simple nonlinear advective problem,we can introduce physically unreal and direct interaction of three or more waves.Numerical tests indicate that this phenomenon has certain influence on the simulated results of two-dimensional Benard convection.
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