Parallel computation of three-dimensional flows using overlapping grids with adaptive mesh refinement

Abstract

This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid within the overlapping grid structure and its associated refinement grids can be independently partitioned over a chosen set of processors. A modified bin-packing algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors. All components of the AMR algorithm such as error estimation, regridding, and interpolation are performed in parallel.The parallel time-stepping algorithm is illustrated for initial-boundary-value problems involving a linear advectiondiffusion equation and the (nonlinear) reactive Euler equations. Numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach. Exact solutions of the advection-diffusion equation are constructed, and these are used to check the corresponding numerical solutions for a variety of tests involving different overlapping grids, different numbers of refinement levels and refinement ratios, and different numbers of processors. The problem of planar shock diffraction by a sphere is considered as an illustration of the numerical approach for the Euler equations, and a problem involving the initiation of a detonation from a hot spot in a T-shaped pipe is considered to demonstrate the numerical approach for the reactive case. For both problems, the solutions are shown to be well resolved on the finest grid. The parallel performance of the approach is examined in detail for the shock diffraction problem.

THREE-DIMENSIONAL SOLARWINDMODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID

“…The cubed sphere (Ronchi et al 1996), which constitutes a spherical surface with six non-overlapping components, is another overset grid recently used for the numerical study of mantle convection, thermal convection, and shallow water (Hernlund & Tackley 2003;Choblet 2005;Chen & Xiao 2008). Based on the concept of an overset grid (Chesshire & Henshaw 1990), Henshaw & Schwendeman (2008) proposed a numerical solution approach for nonlinear evolutionary partial differential equations in complex 3D domains, where the domains are represented by overlapping structured grids, and block-structured AMR is used to locally increase the spatial resolution. Usmanov (1996) also introduced a composite mesh in his 3D solar wind modeling.…”

Fluid-structure interaction modeling with chimera grids in NSMB

“…The huge possibilities offered by this approach explain its successful use in many and diverse applications like high-speed reaction flow, blood flow, combustion, aerodynamics, flow around ships, separation of the spacecraft orbiter from boosters or aerodynamic noise. It is associated with other numerical tools to increase efficiency (such as Automatic Mesh Refinement (AMR) coupling with chimera method [9] for example). The chimera process is detailed for structured grids by Thompson [17].…”

Efficient parallelization of a regional ocean model for the western Mediterranean Sea

“…It also enables a better representation of the topographical features of the ocean basin, such as the Strait of Gibraltar and the Strait of Messina, offering high resolution for specific areas. Some regular meshes try to solve this problem by using an unstructured mesh refinement to locally increase the resolution (Henshawa and Schwendemanb, 2008).…”

“…Other authors rely on libraries, such as Cowles (2008) Aggregating the simulation results of each submesh does not yield the same result as simulating the original full mesh, in other words, completely separate calculations for each submesh are not possible. As shown in Figure 3 every slave also needs to consult and compute points around its submesh, known as ghost points (Luong et al, 2004;Henshawa and Schwendemanb, 2008;Tseng and Chien, 2011) orhalo points (Sannino et al, 2001;Cowles, 2008;Wang et al, 2010). This implies not only more redundant computationin the slaves, as can be seen in the following algorithm description, but also the need to exchange some data between neighbouring slaves through the master at every time step.…”