An implementation of the direct-forcing immersed boundary method using GPU power

Abstract

A graphics processing unit (GPU) is utilized to apply the direct-forcing immersed boundary method. The code running on the GPU is generated with the help of the Compute Unified Device Architecture (CUDA). The first and second spatial derivatives of the incompressible Navier-Stokes equations are discretized by the sixth-order central compact finite-difference schemes. Two flow fields are simulated. The first test case is the simulated flow around a square cylinder, with the results providing good estimations of the wake region mechanics and vortex shedding. The second test case is the simulated flow around a circular cylinder. This case was selected to better understand the effects of sharp corners on the force coefficients. It was observed that the estimation of the force coefficients did not result in any troubles in the case of a circular cylinder. Additionally, the performance values obtained for the calculation time for the solution of the Poisson equation are compared with the values for other CPUs and GPUs from the literature. Consequently, approximately 3× and 20× speedups are achieved in comparison with GPU (using CUSP library) and CPU, respectively. CUSP is an open-source library for sparse linear algebra and graph computations on CUDA.

A Stress Mapping Immersed Boundary Method for Viscous Flows

“…After obtaining the pressure and velocity fields, the Cauchy stress tensor can be calculated at grid nodes that are relevant to the mapping process according to Eq. (18). Note that the shape functions integrals in Eq.…”

“…Various approaches are found in the literature of immersed boundary methods for treating this issue. In a continuous forcing approach, source terms are added to the governing equations, and have effect only near the interface [15][16][17][18]. Goldstein et al, [19] introduced another forcing term for the aim of having a velocity feedback control.…”

Simulations of self-propelled anguilliform swimming using the immersed boundary method in OpenFOAM

“…The reduction of computational cost is contributed by one of the CONTACT Hui Feng E0013532@u.nus.edu reasons: there is almost no cost for the mesh regeneration in each individual step (Dillon & Li, 2009); it is much easier to describe a complex motion of the body relative to a fixed domain mesh (Mittal & Iaccarino, 2005); and many mature methods, solver packages, and algorithms developed for Cartesian grids are available. Following this strategy, a variety of refinements and modifications of the IBM have been developed during the past few decades (Diao et al, 2018;Dillon & Li, 2009;Hopkins, Vanderlei, & Fauci, 2012;Mittal & Iaccarino, 2005;Peskin, 2003;Tutkun & Edis, 2017). With proper methods being used to program the IBM solvers, several FSI problems have been solved (Ardekani & Brandt, 2019;Coclite, Ranaldo, de Tullio, Decuzzi, & Pascazio, 2019).…”