A second order time-stepping scheme for parabolic interface problems with moving interfaces
A second order time-stepping scheme for parabolic interface problems with moving interfaces
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DOI：
10.1051/m2an/2016072
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发表时间：
2017-07
期刊：
影响因子：
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通讯作者：
S. Frei;T. Richter
中科院分区：
文献类型：
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作者：
S. Frei;T. Richter
本文提出了一个求解运动区域和界面上抛物问题的二阶时间推进格式。扩散系数是不连续的，并且跨越内部界面跳跃。这导致解在空间和时间上具有不连续的导数。如果不对界面进行特殊处理，空间和时间离散化都将是次优的。对于这样的问题，我们开发了一个时间步长的方法，基于cG（1）欧拉时空Galerkin方法。我们显示-无论是解析和数值-二阶收敛的时间。获得最佳收敛顺序的关键是使用与移动界面对齐的时空测试函数和试验函数。可能的应用是多相流或流体-结构相互作用问题。
We present a second order time-stepping scheme for parabolic problems on moving domains and interfaces. The diffusion coefficient is discontinuous and jumps across an interior interface. This causes the solution to have discontinuous derivatives in space and time. Without special treatment of the interface, both spatial and temporal discretization will be sub-optimal. For such problems, we develop a time-stepping method, based on a cG(1) Eulerian space-time Galerkin approach. We show −both analytically and numerically− second order convergence in time. Key to gaining the optimal order of convergence is the use of space-time test- and trial-functions, that are aligned with the moving interface. Possible applications are multiphase flow or fluid-structure interaction problems.