A method for implementing Dirichlet and third‐type boundary conditions in PTRW simulations
A method for implementing Dirichlet and third‐type boundary conditions in PTRW simulations
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DOI：
10.1002/2013wr013796
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发表时间：
2014-02
影响因子：
5.4
通讯作者：
J. Koch;Wolfgang Nowak
中科院分区：
文献类型：
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作者：
J. Koch;Wolfgang Nowak
我们提出了一种有效和精确的数值方法，用于在对流弥散输运的粒子跟踪随机行走（PTRW）模拟中实现Dirichlet边界条件。这是一个挑战，因为定义Dirichlet边界条件的浓度需要调用某种控制体积，这对于基于拉格朗日的PTRW概念来说是不自然的。我们的方法将基于PTRW的粒子密度的Galerkin投影到离散边界的控制体积上。因此，我们在边界条件下获得浓度值，并且可以控制颗粒释放速率，使得满足规定的边界值。这允许复杂形状的内部和外部边界，其中浓度值固定为规定值。第三类边界条件也可以解决。我们测试和说明我们的方法在一系列的测试用例的属性和行为。结果是基准对概念上相关的半解析方法MASST（多解析源叠加技术）和有限元法（FEM）。MASST由于其解析解的限制只能用于均匀速度场，而FEM由于离散化范围内的数值离散而只能用于大Péclet数的非均匀速度场。结果表明，我们提出的方法在这两个政权比其他方法表现得更好。
We present an efficient and accurate numerical method for implementing Dirichlet boundary conditions in particle tracking random walk (PTRW) simulations of advective‐dispersive transport. This is a challenge, because defining concentrations for Dirichlet boundary conditions requires invoking control volumes of some kind, which are not natural to the Lagrangian‐based PTRW concept. Our method performs a Galerkin projection of PTRW‐based particle densities onto control volumes that discretize the boundary. Thus, we obtain concentration values at the boundary condition and can control the particle release rates such that the prescribed boundary values are met. This allows for complex‐shaped internal and external boundaries, where concentration values are fixed to prescribed values. Third‐type boundary conditions can be addressed as well. We test and illustrate the properties and behavior of our method in a series of test cases. The results are benchmarked against the conceptually related semianalytical method MASST (multiple analytical source superposition technique) and to those of a finite element method (FEM). While MASST is restricted to uniform velocity fields due to the underlying analytical solutions, FEM is limited in heterogeneous velocity fields at large Péclet numbers by numerical dispersion in the feasible discretization range. The results demonstrate that our proposed method performs better than the other methods in both regimes.