The convective-diffusive equations are highly nonlinear. In one-dimensional flow, high order difference scheme or exponential scheme can be used to reduce the error. However, in two or three-dimensional flow, these methods are not suitable, because diffusion occurs at both streamlinewise and cross streamlinewise. The skew upwind scheme has advantages in reducing cross streamlinewise numerical diffusion but often becomes unstable and are too complex to extend to three diemsnion flows.
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