论文标题
多孔介质流的投影方法
A projection method for porous media flow
论文作者
论文摘要
从大规模地球物理到细胞生物学的各种自然环境中，流过多孔的弹性变形介质。在不可压缩的成分的情况下，孔隙压力充当一种拉格朗日乘数，以满足对流体差异的限制。所得的方程系统可能是一个非线性的鞍点问题，并且难以在数值上求解，需要非线性隐式求解器或通量分解方法。在这里，我们提出了一种通过多孔介质及其耦合弹性变形的流动模拟的方法。通过类似于Chorin投影方法的方式校正试验速度，在每个时间步骤中计算孔隙压力场。我们证明了该方法在空间和时间上的二阶收敛性，并将其应用于新霍克凝胶的相位分离。
Flow through porous, elastically deforming media is present in a variety of natural contexts ranging from large-scale geophysics to cellular biology. In the case of incompressible constituents, the porefluid pressure acts as a Lagrange multiplier to satisfy the resulting constraint on fluid divergence. The resulting system of equations is a possibly non-linear saddle-point problem and difficult to solve numerically, requiring nonlinear implicit solvers or flux-splitting methods. Here, we present a method for the simulation of flow through porous media and its coupled elastic deformation. The pore pressure field is calculated at each time step by correcting trial velocities in a manner similar to Chorin projection methods. We demonstrate the method's second-order convergence in space and time and show its application to phase separating neo-Hookean gels.
