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首页> 外文期刊>Journal of Computational Physics >SPACE-TIME INTEGRATED LEAST-SQUARES - SOLVING A PURE ADVECTION EQUATION WITH A PURE DIFFUSION OPERATOR
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SPACE-TIME INTEGRATED LEAST-SQUARES - SOLVING A PURE ADVECTION EQUATION WITH A PURE DIFFUSION OPERATOR

机译：时空积分最小二乘-用纯扩散算子求解纯平均方程

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摘要

An alternative formulation for multidimensional scalar advection is derived following both a conservative and a variational approach, by applying the least-squares method simply generalized to the space-time domain. In the space-time framework pure advection is regarded as a process involving only anisotropic diffusion along space-time characteristics. The resulting parabolic-type equation lends itself to a straightforward Galerkin integration that yields a symmetric, diagonally dominant, positive, and unconditionally stable operator. The conditions of equivalence between the advective problem and its parabolized counterpart are established by using standard variational theory in anisotropic Sobolev spaces specially designed for advection equations. To demonstrate the general applicability of the method, ''parabolized advection'' is simulated in 2D manifolds embedded in 3D and 4D space-time domains. (C) 1995 Academic Press, Inc. [References: 17]
机译：通过应用简单概括到时空域的最小二乘法，既遵循保守方法又采用变分方法，可以得出多维标量对流的替代公式。在时空框架中，纯对流被认为是仅沿时空特征各向异性扩散的过程。所得的抛物线型方程式使其易于直接进行Galerkin积分，从而产生对称，对角占优势，正且无条件稳定的算子。在标准为对流方程设计的各向异性Sobolev空间中，使用标准变分理论建立了对流问题及其抛物线对应物之间的等价条件。为了证明该方法的一般适用性，在嵌入3D和4D时空域的2D歧管中模拟了“代谢平流”。 （C）1995 Academic Press，Inc. [参考：17]

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