An adaptive wavelet-collocation method for shock computations

Regele, Jonathan D.; Vasilyev, Oleg V.

doi:10.1080/10618560903117105

Cited by 53 publications

(37 citation statements)

References 45 publications

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“…In addition to providing a framework for solving partial differential equations, they can be adapted to multiresolution geometrical representations using level sets [11]. More recently an adaptive wavelet collocation method was applied to simulations of shocks interacting with interfaces [12] demonstrating how the wavelet coefficients can be used to detect the emergence of localized structures.…”

Section: Introductionmentioning

confidence: 99%

High order finite volume methods on wavelet-adapted grids with local time-stepping on multicore architectures for the simulation of shock-bubble interactions

Hejazialhosseini

Rossinelli

Bergdorf

et al. 2010

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

High order finite volume methods on wavelet-adapted grids with local time-stepping on multicore architectures for the simulation of shock-bubble interactions

Hejazialhosseini

Rossinelli

Bergdorf

et al. 2010

Journal of Computational Physics

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“…The adaptive wavelet collocation method is a general method for the solution of a large class of linear and nonlinear partial differential equations (Vasilyev and Bowman 2000;Vasilyev 2003;Vasilyev and Kevlahan 2005;Regele and Vasilyev 2009). The method has already been successfully applied in wide range of fluid mechanics problems, e.g., that of Vasilyev et al (1997), Vasilyev and Kevlahan (2002), Kevlahan et al (2007), Reckinger et al (2010), and Schneider and Vasilyev (2010).…”

Section: Adaptive Wavelet Collocation Methodsmentioning

confidence: 99%

Adaptive volume penalization for ocean modeling

2012

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The development of various volume penalization techniques for use in modeling topographical features in the ocean is the focus of this paper. Due to the complicated geometry inherent in ocean boundaries, the stair-step representation used in the majority of current global ocean circulation models causes accuracy and numerical stability problems. Brinkman penalization is the basis for the methods developed here and is a numerical technique used to enforce no-slip boundary conditions through the addition of a term to the governing equations. The second aspect to this proposed approach is that all governing equations are solved on a nonuniform, adaptive grid through the use of the adaptive wavelet collocation method. This method solves the governing equations on temporally and spatially varying meshes, which allows higher effective resolution to be obtained with less computational cost. When penalization methods are coupled with the adaptive wavelet collocation method, the flow near the boundary can be well-resolved. It is especially useful for simulations of boundary currents and tsunamis, where flow near the boundary is important. This paper will give a thorough analysis of these methods applied to the shallow water equations, as well as some preliminary work applying these methods to volume penalization for bathymetry representation for use in either the nonhydrostatic or hydrostatic primitive equations.

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“…Many attractive mathematical properties of the wavelet multiresolution analysis such as compression, denoising, and multi-scale decomposition have made it a very promising tool in the challenging search for robust and computationally efficient multi-scale computational approach for modeling and simulation. Adaptive Wavelet Collocation Method (AWCM) is such a technique, which has been developed and thoroughly investigated for parabolic [1,2], hyperbolic [3], and elliptic [4] partial differential equations. It was successfully applied to a wide spectrum of problems including incompressible [5], compressible subsonic [6] and supersonic [3] flows, wavelet-based Adaptive Large Eddy Simulation [7,8,9,10,11,12,13], thermoacoustic wave propagation [14], Rayleigh-Taylor instability [15], ocean modeling [16], combustion [17], fluid-structure interactions [18,19], viscoelastic and poroviscoelastic flows [20,21,22].…”

Section: Introductionmentioning

confidence: 99%

“…Adaptive Wavelet Collocation Method [1, 2,3,4] is based on the "second generation wavelets" [23,24]. In AWCM, the partial differential equations are solved in physical space on an adaptive nested (dyadic) computational grid.…”

Section: Introductionmentioning

confidence: 99%

Parallel adaptive wavelet collocation method for PDEs

Nejadmalayeri¹,

Vezolainen

Brown-Dymkoski

et al. 2015

Journal of Computational Physics

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Please cite this article in press as: A. Nejadmalayeri et al., Parallel adaptive wavelet collocation method for PDEs, J. Comput. Phys. (2015), http://dx. AbstractA parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogenous turbulence with linear forcing at effective non-adaptive resolutions up to 2048 3 using as many as 2048 CPU cores.

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An adaptive wavelet-collocation method for shock computations

Cited by 53 publications

References 45 publications

High order finite volume methods on wavelet-adapted grids with local time-stepping on multicore architectures for the simulation of shock-bubble interactions

High order finite volume methods on wavelet-adapted grids with local time-stepping on multicore architectures for the simulation of shock-bubble interactions

Adaptive volume penalization for ocean modeling

Parallel adaptive wavelet collocation method for PDEs

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