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首页> 外文期刊>Journal of Computational Physics >Energy stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition
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Energy stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition

机译：基于重叠域分解的双曲型偏微分方程的能量稳定数值方法。

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摘要

Overlapping domain decomposition methods, otherwise known as overset grid or chimera methods, are useful for simplifying the discretization of partial differential equations in or around complex geometries. Though in wide use, such methods are prone to numerical instability unless numerical diffusion or some other form of regularization is used, especially for higher-order methods. To address this shortcoming, high-order, provably energy stable, overlapping domain decomposition methods are derived for hyperbolic initial boundary value problems. The overlap is treated by splitting the domain into pieces and using generalized summation-by-parts derivative operators and polynomial interpolation. New implicit and explicit operators are derived that do not require regularization for stability in the linear limit. Applications to linear and nonlinear problems in one and two dimensions are presented, where it is found the explicit operators are preferred to the implicit ones.
机译：重叠域分解方法（也称为重叠网格或嵌合方法）可用于简化复杂几何体中或周围的偏微分方程的离散化。尽管广泛使用，但除非使用数值扩散或其他形式的正则化，否则此类方法易于出现数值不稳定，尤其是对于高阶方法而言。为了解决这个缺点，针对双曲型初始边值问题推导了高阶，证明是能量稳定的，重叠域分解方法。通过将域拆分为多个部分，并使用广义的逐部分求和运算符和多项式插值法来处理重叠。派生出新的隐式和显式运算符，它们不需要正则化就可以保证线性极限的稳定性。介绍了在一维和二维线性和非线性问题的应用，发现显式算子优于隐式算子。

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