论文标题
多分辨率格林的功能方法不可压缩流
Multi-resolution lattice Green's function method for incompressible flows
论文作者
论文摘要
我们提出了一种多分辨率策略，该策略与晶格绿色功能（LGF）技术兼容，以解决无限域上的粘性，不可压缩的流动。 LGF方法利用有限体积方案在正式无界的笛卡尔网格上的规律性，以产生健壮和计算有效的解决方案。原始方法在空间上是自适应的，但是与嵌入式网状细胞的整合挑战，因为仅针对固定分辨率定义了基础LGF。我们提出了一种用于自适应网状细化的ANSATZ，其中使用LGF技术在复合网格上近似于由一系列不同分辨率的无限晶格构建的复合网格上的LGF技术近似。为了求解不可压缩的Navier-Stokes方程，这进一步与粘性术语的集成因子结合在一起，以及适合由此产生的差分偏见方程的适当的runge-kutta方案。通过对涡旋环的数值模拟来验证并行的算法，并模拟了高雷诺数在高雷诺数处的涡流碰撞，以证明可以通过空间和改进适应性来实现的计算细胞的减少。
We propose a multi-resolution strategy that is compatible with the lattice Green's function (LGF) technique for solving viscous, incompressible flows on unbounded domains. The LGF method exploits the regularity of a finite-volume scheme on a formally unbounded Cartesian mesh to yield robust and computationally efficient solutions. The original method is spatially adaptive, but challenging to integrate with embedded mesh refinement as the underlying LGF is only defined for a fixed resolution. We present an ansatz for adaptive mesh refinement, where the solutions to the pressure Poisson equation are approximated using the LGF technique on a composite mesh constructed from a series of infinite lattices of differing resolution. To solve the incompressible Navier-Stokes equations, this is further combined with an integrating factor for the viscous terms and an appropriate Runge-Kutta scheme for the resulting differential-algebraic equations. The parallelized algorithm is verified through with numerical simulations of vortex rings, and the collision of vortex rings at high Reynolds number is simulated to demonstrate the reduction in computational cells achievable with both spatial and refinement adaptivity.
