Improved numerical method for three dimensional diffusion equation with strongly discontinuous coefficients
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摘要: 针对惯性约束聚变领域需要求解的含强间断导热系数的扩散方程，借鉴各向异性导热的思想，给出了一种导热系数定义在网格节点的支撑算子改进格式。改进后的方法保留了支撑算子格式的算子相容性优点。数值算例表明，新方法可以很好地处理含强间断和强非线性的热扩散问题，计算结果保持较高的精度，适合于辐射流体力学问题的模拟。Abstract: The numerical heat barrier is induced when the traditional support operator method is used to solve the diffusion equation with strongly discontinuous coefficients. In this paper, a new support operator method is proposed. In this method, anisotropy conductivity tensors are introduced and defined on grid vertices. The method is applied to two diffusion cases with strongly discontinuous conductivity coefficients. The numerical results agree well with the analytical values, which proves the feasibility of the proposed scheme to solve the diffusion equation with strongly discontinuous coefficients.
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