A high order compact time/space finite difference scheme for the 2D and 3D wave equation with a damping layer

Kahana, Adar; Smith, Fouche; Turkel, Eli; Tsynkov, Semyon

doi:10.1016/j.jcp.2022.111161

Cited by 3 publications

(1 citation statement)

References 20 publications

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“…We remark that alternative methods exist for high-order simulations on unbounded domains, but available methodologies are limited to the linear case without like-for-like efficiency comparisons, 26 concern elliptic problems, 27 or lack formal stability analyses. 28 Recent studies 20,29 introduced adaptive methods based on time-evolving distributions of Laguerre and Hermite collocation points for simulations on unbounded domains and applied them within spectrally adaptive neural network models.…”

Section: Introductionmentioning

confidence: 99%

Efficient hyperbolic–parabolic models on multi‐dimensional unbounded domains using an extended DG approach

Vismara,

Benacchio

2023

Numerical Methods in Fluids

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We introduce an extended discontinuous Galerkin discretization of hyperbolic–parabolic problems on multidimensional semi‐infinite domains. Building on previous work on the one‐dimensional case, we split the strip‐shaped computational domain into a bounded region, discretized by means of discontinuous finite elements using Legendre basis functions, and an unbounded subdomain, where scaled Laguerre functions are used as a basis. Numerical fluxes at the interface allow for a seamless coupling of the two regions. The resulting coupling strategy is shown to produce accurate numerical solutions in tests on both linear and nonlinear scalar and vectorial model problems. In addition, an efficient absorbing layer can be simulated in the semi‐infinite part of the domain in order to damp outgoing signals with negligible spurious reflections at the interface. By tuning the scaling parameter of the Laguerre basis functions, the extended DG scheme simulates transient dynamics over large spatial scales with a substantial reduction in computational cost at a given accuracy level compared to standard single‐domain discontinuous finite element techniques.

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Section: Introductionmentioning

confidence: 99%

Efficient hyperbolic–parabolic models on multi‐dimensional unbounded domains using an extended DG approach

Vismara,

Benacchio

2023

Numerical Methods in Fluids

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High Order Solution to Exterior 3D Wave Equation by the Method of Difference Potentials

Smith

Tsynkov

Turkel

2022

Lecture Notes in Computational Science and Engineering

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Novel hybrid compact schemes for stream function–velocity formulation of the incompressible Navier–Stokes equations

Yadav

Maurya

Maurya³

et al. 2023

Physics of Fluids

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In this paper, we have developed new hybrid compact schemes for the simulation of stream function-velocity formulation of the two-dimensional incompressible Navier-Stokes equation. The first-order spatial derivatives are approximated by the optimized upwind compact scheme, and the Laplacian and biharmonic operators are discretized using fourth-order hybrid compact schemes. Moreover, we have also performed Fourier analysis to assess the resolution and added numerical diffusion properties of numerical schemes for stream function-velocity formulation of the linear Navier-Stokes equation. For time discretization, we have used explicit fourth-stage fourth-order Runge-Kutta method and hybrid filters. Furthermore, to validate the accuracy and efficiency of the schemes, several fluid flow problems, including a test problem with a non-homogeneous source term and a lid-driven cavity problem, are considered. Numerical results exhibit a great match to the results reported in the literature at lower computational cost with hybrid filters.

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A high order compact time/space finite difference scheme for the 2D and 3D wave equation with a damping layer

Cited by 3 publications

References 20 publications

Efficient hyperbolic–parabolic models on multi‐dimensional unbounded domains using an extended DG approach

Efficient hyperbolic–parabolic models on multi‐dimensional unbounded domains using an extended DG approach

High Order Solution to Exterior 3D Wave Equation by the Method of Difference Potentials

Novel hybrid compact schemes for stream function–velocity formulation of the incompressible Navier–Stokes equations

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