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《Chinese Journal of Atmospheric Sciences》 1982-01
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THE CONSTRUCTION AND APPLICATION OF DIFFERENCE SCHEMES OF EVOLUTION EQUATIONS

Ji Zhong-zhen Zeng Qing-cun (Institute of Atmospheric Physics, Academia Sinica)  
In this paper, many quasi-linear equations are reduced to evolution equations inoperator form It is proved that if the operator A is non-negative, then"strongly implicit (i.e., 1/2 ≤θ≤ 1) schemes" would be absolutely stable, but if the operator A is skew-symmetric, then "weakly implicit and explicit (i.e., 0 ≤θ ≤ 1/2) schemes" are absolutely unstable.Furthermore, taking one dimensional non-linear advection equation as an example, three schemes with non-negative operator A and the corresponding stable schemes with an artificial dissipation term are designed. A computational example is given. It is shown that the latter schemes are effective for damping false parasitic waves, and suitable for the calculation of problems with discontinuity.
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