A new grid structure for domain extension

Zhu, Bo; Lu, Wenlong; Cong, Matthew; Kim, Byung Moon; Fedkiw, Ronald

doi:10.1145/2461912.2461999

Cited by 51 publications

(40 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the mesh based methods, finite volume methods [11][12][13][14] and finite difference methods [18][19] have been extensively used. In order to handle large domains, a multi-resolution capability and far-field boundary conditions to the regular fixed-grid NS solver have also been proposed using chimera and moving grid methods [15][16][17]. The advantage of such a strategy is the use of regular grids that could avoid the numerical stability issues; however, if viscous effects are introduced then there will be a restriction on the length time step.…”

Section: Introductionmentioning

confidence: 99%

A hybrid method for modelling two dimensional non-breaking and breaking waves

Sriram

Schlurmann

2014

Journal of Computational Physics

View full text Add to dashboard Cite

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractThis is the first paper to present a hybrid method coupling a Improved Meshless Local Petrov Galerkin method with Rankine source solution (IMLPG_R) based on the Navier Stokes (NS) equations, with a finite element method (FEM) based on the fully nonlinear potential flow theory (FNPT) in order to efficiently simulate the violent waves and their interaction with marine structures. The two models are strongly coupled in space and time domains using a moving overlapping zone, wherein the information from both the solvers is exchanged. In the time domain, the Runge-Kutta 2 nd order method is nested with a predictor-corrector scheme. In the space domain, numerical techniques including 'Feeding Particles' and two-layer particle interpolation with relaxation coefficients are introduced to achieve the robust coupling of the two models. The properties and behaviours of the new hybrid model are tested by modelling a regular wave, solitary wave and Cnoidal wave including breaking and overtopping. It is validated by comparing the results of the method with analytical solutions, results from other methods and experimental data. The paper demonstrates that the method can produce satisfactory results but uses much less computational time compared with a method based on the full NS model.

show abstract

Section: Introductionmentioning

confidence: 99%

A hybrid method for modelling two dimensional non-breaking and breaking waves

Sriram

Schlurmann

2014

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…Another quite useful, albeit more restrictive, approach to spatial adaptivity is the use of stretched grid cells. For example, portions of a regularly sampled domain may be replaced with tall cells that have been stretched along a single axis [Chentanez and Müller 2011;Irving et al 2006], or larger sections of a regular grid may be stretched along multiple axes by essentially translating entire grid lines [Zhu et al 2013]. These approaches preserve most of the regular grid efficiency while offering some benefits of adaptivity.…”

Section: Related Workmentioning

confidence: 99%

Power diagrams and sparse paged grids for high resolution adaptive liquids

et al. 2017

View full text Add to dashboard Cite

Fig. 1. (Left)Water filling a river bed surrounded by a canyon, with effective resolution 512 2 × 1024. Three refinement levels are used, based on proximity to the terrain. (Right) Sources inject water into a container and collide to form a thin sheet, with effective resolution 512 3 . Adaptivity pattern shown on background.We present an efficient and scalable octree-inspired fluid simulation framework with the flexibility to leverage adaptivity in any part of the computational domain, even when resolution transitions reach the free surface. Our methodology ensures symmetry, definiteness and second order accuracy of the discrete Poisson operator, and eliminates numerical and visual artifacts of prior octree schemes. This is achieved by adapting the operators acting on the octree's simulation variables to reflect the structure and connectivity of a power diagram, which recovers primal-dual mesh orthogonality and eliminates problematic T-junction configurations. We show how such operators can be efficiently implemented using a pyramid of sparsely populated uniform grids, enhancing the regularity of operations and facilitating parallelization. A novel scheme is proposed for encoding the topology of the power diagram in the neighborhood of each octree cell, allowing us to locally reconstruct it on the fly via a lookup table, rather than resorting to costly explicit meshing. The pressure Poisson equation is solved via a highly efficient, matrix-free multigrid preconditioner for Conjugate Gradient, adapted to the power diagram discretization. We use another sparsely † M. Aanjaneya and M. Gao are joint first authors. * M. Aanjaneya was with the University of Wisconsin -Madison during this work. This work was supported in part by National Science Foundation grants IIS-1253598, CCF-1423064, CCF-1533885 and by the Natural Sciences and Engineering Research Council of Canada under grant RGPIN-04360-2014. The authors are grateful to Nathan Mitchell for his indispensable help with modeling and rendering of examples. C. Batty would like to thank Ted Ying for carrying out preliminary explorations on quadtrees. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. populated uniform grid for high resolution interface tracking with a narrow band level set representation. Using the recently introduced SPGrid data structure, sparse uniform grids in both the power diagram discretization and our narrow band level set can be compactly stored and efficiently updated via streaming operations. Additionally, we present enhancem...

show abstract

“…In the meshless methods, the fluid particles are largely followed and so the methods are also referred to as particle methods. The mesh-based methods have been developed for several decades and mainly based on finite volume and finite different methods (Greaves 2010;Causon et al 2010;Chen et al 2010;Zhu et al 2013). The meshless (or particle) methods are of relative new development, but have been recognized as promising alternative methods in recent years, particularly for modelling violent waves and their interaction with structures owing to their advantages that meshes are not required and numerical diffusion associated with convection terms is eliminated in contrast to mesh-based methods.…”

Section: Introductionmentioning

confidence: 99%

“…A brief overview for meshless methods is given below, as this paper is concerned only on topics related to them. For more information about mesh-based methods, the readers are referred to other publications, such as Causon et al (2010) and Zhu et al (2013).…”

Section: Introductionmentioning

confidence: 99%

A review on approaches to solving Poisson’s equation in projection-based meshless methods for modelling strongly nonlinear water waves

Zhou

Yan

2016

J. Ocean Eng. Mar. Energy

View full text Add to dashboard Cite

Three meshless methods, including incompressible smooth particle hydrodynamic (ISPH), moving particle semi-implicit (MPS) and meshless local Petrov-Galerkin method based on Rankine source solution (MLPG_R) methods, are often employed to model nonlinear or violent water waves and their interaction with marine structures. They are all based on the projection procedure, in which solving Poisson's equation about pressure at each time step is a major task. There are three different approaches to solving Poisson's equation, i.e. (1) discretizing Laplacian directly by approximating the second-order derivatives, (2) transferring Poisson's equation into a weak form containing only gradient of pressure and (3) transferring Poisson's equation into a weak form that does not contain any derivatives of functions to be solved. The first approach is often adopted in ISPH and MPS, while the third one is implemented by the MLPG_R method. This paper attempts to review the most popular, though not all, approaches available in literature for solving the equation.

show abstract

A new grid structure for domain extension

Cited by 51 publications

References 34 publications

A hybrid method for modelling two dimensional non-breaking and breaking waves

A hybrid method for modelling two dimensional non-breaking and breaking waves

Power diagrams and sparse paged grids for high resolution adaptive liquids

A review on approaches to solving Poisson’s equation in projection-based meshless methods for modelling strongly nonlinear water waves

Contact Info

Product

Resources

About