A Full-Depth Amalgamated Parallel 3D Geometric Multigrid Solver for GPU Clusters

Numerical computations of incompressible flow equations with pressure-based algorithms necessitate the solution of an elliptic Poisson equation, for which multigrid methods are known to be very efficient. In our previous work we presented a dual-level (MPI-CUDA) parallel implementation of the Navier-Stokes equations to simulate buoyancy-driven incompressible fluid flows on GPU clusters with simple iterative methods while focusing on the scalability of the overall solver. In the present study we describe the implementation and performance of a multigrid method to solve the pressure Poisson equation within our MPI-CUDA parallel incompressible flow solver. Various design decisions and algorithmic choices for multigrid methods are explored in light of NVIDIA’s recent Fermi architecture. We discuss how unique aspects of an MPI-CUDA implementation for GPU clusters is related to the software choices made to implement the multigrid method. We propose a new coarse grid solution method of embedded multigrid with amalgamation and show that the parallel implementation retains the numerical efficiency of the multigrid method. Performance measurements on the NCSA Lincoln and TACC Longhorn clusters are presented for up to 64 GPUs

An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver

We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the pseudo-compressibility method recently proposed by Guermond and Minev [Comptes Rendus Mathematique, 348:581-585, 2010] that uses a directional splitting strategy to discretize the incompressible Navier-Stokes equations, thereby reducing the linear systems to a series of one-dimensional tridiagonal systems. We perform numerical simulations of several fluid-structure interaction problems in two and three dimensions and study the accuracy and convergence rates of the proposed algorithm. For these problems, we compare the proposed algorithm against other second-order projection-based fluid solvers. Lastly, the strong and weak scaling properties of the proposed algorithm are investigated

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3,700 are used to verify the accuracy and physical fidelity of the formulation.Comment: 32 pages, 9 figures; preprint submitted to Journal of Computational Physic

Simulation of flows with violent free surface motion and moving objects using unstructured grids

This is the peer reviewed version of the following article: [Löhner, R. , Yang, C. and Oñate, E. (2007), Simulation of flows with violent free surface motion and moving objects using unstructured grids. Int. J. Numer. Meth. Fluids, 53: 1315-1338. doi:10.1002/fld.1244], which has been published in final form at https://doi.org/10.1002/fld.1244. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms are used to obtain velocities and pressure in the gas region near the free surface. The VOF technique is validated against the classic dam-break problem, as well as series of 2D sloshing experiments and results from SPH calculations. These and a series of other examples demonstrate that the ability of the present approach to simulate violent free surface flows with strong nonlinear behaviour.Peer ReviewedPostprint (author's final draft