平流改进了一维非均匀介质中连续扩散的均匀化模型
Advection improves homogenized models of continuum diffusion in one-dimensional heterogeneous media
摘要：
我们提出了一种替代方法的一维连续扩散模型的空间可变（异质）扩散。我们的方法，扩展了最近的工作随机扩散，假设常数系数均匀化方程的形式的对流扩散方程的有效（扩散率和速度）系数。为了计算有效系数，我们的方法涉及解决两个非耦合的边界值问题的非均匀介质，并导致系数取决于空间变化的扩散率（像往常一样），以及对非均匀模型施加的边界条件。计算实验比较我们的对流扩散均匀化模型的标准均匀化模型表明，包括平流项的均匀化方程导致改进的近似原始非均质模型的解决方案。
英文摘要：
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized equation takes the form of an advection-diffusion equation with effective (diffusivity and velocity) coefficients. To calculate the effective coefficients, our approach involves solving two uncoupled boundary value problems over the heterogeneous medium and leads to coefficients depending on the spatially-varying diffusivity (as usual) as well as the boundary conditions imposed on the heterogeneous model. Computational experiments comparing our advection-diffusion homogenized model to the standard homogenized model demonstrate that including an advection term in the homogenized equation leads to improved approximations of the solution of the original heterogeneous model.
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