Bucket-based multigrid preconditioner for solving pressure Poisson equation using a particle method

Södersten, Axel; Matsunaga, Takuya; Koshizuka, Seiichi

doi:10.1016/j.compfluid.2019.104242

Cited by 4 publications

(7 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This would bring another advantage of high parallel efficiency in large-scale simulations. Because the DPs are linked to the background meshes, any acceleration solver for the linear system can be applied, such as a bucket-based multigrid preconditioner used in a conventional particle method (Södersten et al, 2019). Moreover, the proposed MCD method could be coupled with a highly efficient parallelization technique using the Cartesian grid system (Jansson et al, 2019).…”

Section: Discussionmentioning

confidence: 99%

A particle-based method using the mesh-constrained discrete point approach for two-dimensional Stokes flows

MATSUDA

TSUKUI

2022

Mechanical Engineering Journal

View full text Add to dashboard Cite

Meshless methods inherently do not require mesh topologies and are practically used for solving continuum equations. However, these methods generally tend to have a higher computational load than conventional mesh-based methods because calculation stencils for spatial discretization become large. In this study, a novel approach for the use of compact stencils in meshless methods is proposed, called the mesh-constrained discrete point (MCD) approach. The MCD approach introduces a Cartesian mesh system to the background of a domain. And the approach rigorously constrains the distribution of discrete points (DPs) in each mesh by solving a dynamic problem with nonlinear constraints. This can avoid the heterogeneity of the DP distribution at the mesh-size level and impose compact stencils with a fixed degree of freedom for derivative evaluations. A fundamental formulation for arrangements of DPs and an application to unsteady Stokes flows are presented in this paper. Numerical tests were performed for the distribution of DPs and flow problems in co-axial and eccentric circular channels. The proposed MCD approach achieved a reasonable distribution of DPs independently of the spatial resolution with a few iterations in pre-processing. Additionally, solutions using the obtained DP distributions in Stokes flow problems were in good agreement with theoretical and reference solutions. The results also confirmed that the numerical accuracies of velocity and pressure achieved the expected convergence order, even when compact stencils were used.

show abstract

Section: Discussionmentioning

confidence: 99%

A particle-based method using the mesh-constrained discrete point approach for two-dimensional Stokes flows

MATSUDA

TSUKUI

2022

Mechanical Engineering Journal

View full text Add to dashboard Cite

show abstract

“…As shown in section 2.3, matrix equation from the PPE needs to be solved in the ISPH method. This procedure is time-consuming and requires a large amount of memory, so we developed a background cell-based geometric multigrid preconditioner following previous studies [7][8][9].…”

Section: Multigrid Methodsmentioning

confidence: 99%

“…There are many examples of application of multigrid methods to numerical methods that use grids or meshes, such as the finite difference method (FDM) [4] and the finite element method (FEM) [6]. However, there are few examples of application of the multigrid method to particle methods [7][8][9], and none to the SPH method used in this study. In this study, we develop a multigrid preconditioning solver for the linear equations of the ISPH method.…”

Section: Introductionmentioning

confidence: 99%

“…In this study, we develop a multigrid preconditioning solver for the linear equations of the ISPH method. Specifically, following previous studies [8,9], we develop a geometric multigrid preconditioning solver that constructs an auxiliary grid based on the background cell used to search for neighboring particles. Then, we compare the number of iterations between the no-preconditioning CG method and the multigrid preconditioning CG method using a dam-breaking problem for incompressible fluids and confirm the effectiveness of the multigrid preconditioning method.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

ISPH with a Geometric Multigrid Preconditioning Solver using Background Cells in GPU environment

Osaki,

Moriwaka,

Asai

2023

VIII International Conference on Particle-Based Methods

View full text Add to dashboard Cite

Incompressible fluid analysis using the ISPH or MPS methods requires the solution of the pressure Poisson equation, which takes up most of the overall computation time. In addition, the iteration number for solving pressure Poisson equations may increase as the simulation model scale increases. This is a common problem in particle methods and the other implicit time integration solvers. In different methods, FEM, etc., good quality preconditioning, such as multigrid preconditioning, can significantly improve the convergence of iterative solution methods. There are two types of multigrid preconditioners, algebraic multigrid and geometric multigrid methods, but there are few examples of their application in particle methods.In this study, we attempted to develop a framework for a geometric multigrid preconditioner for solving the pressure Poisson equation in the ISPH. First, we focused on the geometric multigrid preconditioner using background cells, which are used for neighboring particle search, and implemented it on a GPU environment. Through a simple dam-break problem, we compared the computation time between the Conjugate gradient (CG) solver with a traditional preconditioner and the CG solver with a geometric multigrid preconditioner. We confirmed that the background cell-based geometric multigrid preconditioner is practical for the ISPH method.

show abstract

“…During recent years, increased focus has shifted to improving the computational efficiency of particle methods through a multigrid scheme (Södersten et al, 2019), parallelization (Guo et al, 2018), and running particle methods on graphics processing units (GPUs) (Murotani et al, 2015;Chow et al, 2018). Moreover, several multi-resolution (Tang Axel SÖDERSTEN*, Takuya MATSUNAGA*, Seiichi KOSHIZUKA*, Tomoyuki HOSAKA** and Eiji ISHII* et al, 2016a;Tang et al, 2016b;Chen et al, 2016;Tanaka et al, 2018;Khayyer et al, 2019;Wang et al, 2019) schemes have been proposed, where high spatial resolution is only considered over critical regions of the flow, such as around clearances (Tanaka et al, 2018) and at impact with walls (Chen et al, 2016;Tanaka et al, 2018), rigid structures (Wang et al, 2019) and elastic beams (Khayyer et al, 2019;Khayyer et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

Adaptive resizing-based multi-resolution particle method

Södersten

Matsunaga

Koshizuka

et al. 2022

Mechanical Engineering Journal

Self Cite

View full text Add to dashboard Cite

Multi-resolution techniques are essential for the performance of large-scale simulations of computational fluid dynamics with particle methods. In this study, a novel adaptive multi-resolution scheme has been developed for the least squares moving particle semi-implicit (LSMPS) method. With the proposed technique, particles are dynamically resized based on a local error estimate. The error estimate is defined by how well the velocity of a particle can be approximated by the Taylor-series expansions of its fluid neighbours, and vice versa for wall neighbours. Due to the adaptiveness of the multi-resolution technique, time-consuming optimization of predefined particle size targets is avoided. The adaptiveness also enables particle resizing which tracks transient resolution changes of the flow. Therefore, the adaptiveness should improve the computational efficiency of the multi-resolution method. In this study, the multi-resolution technique was tested for a two-dimensional eccentric rotating cylinder problem with a small clearance and a known steady-state solution. As expected, initially uniform particle sizes quickly decreased around the clearance. The particle size distribution evolution was smooth in both time and space throughout the simulations. Consequently, the multi-resolution method gave significantly more accurate results than a single resolution method with the same number of particles and time-step length. A drawback with the multi-resolution scheme is that the restrictions on time-step lengths become tighter. This issue is considered by an ongoing development of a multi-time stepping scheme.

show abstract

Bucket-based multigrid preconditioner for solving pressure Poisson equation using a particle method

Cited by 4 publications

References 39 publications

A particle-based method using the mesh-constrained discrete point approach for two-dimensional Stokes flows

A particle-based method using the mesh-constrained discrete point approach for two-dimensional Stokes flows

ISPH with a Geometric Multigrid Preconditioning Solver using Background Cells in GPU environment

Adaptive resizing-based multi-resolution particle method

Contact Info

Product

Resources

About