A hybrid method for unsteady inviscid fluid flow

Nordström, Jan; Ham, Frank; Shoeybi, Mohammad; Weide, Edwin Theodorus Antonius van der; Svärd, Magnus; Mattsson, Ken; Iaccarino, Gianluca; Gong, Junbo

doi:10.1016/j.compfluid.2008.09.010

Cited by 23 publications

(15 citation statements)

References 28 publications

(42 reference statements)

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“…The hybrid interface treatment in this sections follows the path set in [45,48]. Since all the hybrid interfaces are handled in a similar manner, we exclusively consider the interface between the north boundary of a finite volume subdomain and the south boundary of a finite difference subdomain.…”

Section: Hybrid Interface Treatmentmentioning

confidence: 99%

“…For all higher order SBP finite difference methods P x and Y N do not match. To satisfy P x = Y N for the higher order methods the control volumes along the hybrid interface must be slightly modified; see Figure 4b and [21,45,48] for more details.…”

Section: Hybrid Interface Treatmentmentioning

confidence: 99%

“…Thus, we take a different approach here and instead use an unstructured, node-centered finite volume method around the geometric complexity. The node-centered finite-volume method was shown to be an SBP scheme in [44] and has been coupled to high order finite difference methods for both advection [45] and advection-diffusion [21,48] problems. Here we extend the coupling to the scalar wave equation (written in first order form for velocities and stresses).…”

Section: Introductionmentioning

confidence: 99%

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Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

OReilly

Nordström

Kozdon

et al. 2015

Commun. Comput. Phys.

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Abstract.A numerical method suitable for wave propagation problems in complex geometries is developed for simulating dynamic earthquake ruptures with realistic friction laws. The numerical method couples an unstructured, node-centered finite volume method to a structured, high order finite difference method. In this work we our focus attention on 2-D antiplane shear problems. The finite volume method is used on unstructured triangular meshes to resolve earthquake ruptures propagating along a nonplanar fault. Outside the small region containing the geometrically complex fault, a high order finite difference method, having superior numerical accuracy, is used on a structured grid. The finite difference method is coupled weakly to the finite volume method along interfaces of collocated grid points. Both methods are on summation-by-parts form. The simultaneous approximation term method is used to weakly enforce the interface conditions. At fault interfaces, fault strength is expressed as a nonlinear function of sliding velocity (the jump in particle velocity across the fault) and a state variable capturing the history dependence of frictional resistance. Energy estimates are used to prove that both types of interface conditions are imposed in a stable manner. Stability and accuracy of the numerical implementation are verified through numerical experiments, and efficiency of the hybrid approach is confirmed through grid coarsening tests. Finally, the method is used to study earthquake rupture propagation along the margins of a volcanic plug. AMS subject classifications: 35L05,35L65,35Q35,65M06,65M08,65M12,65Z05

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Section: Hybrid Interface Treatmentmentioning

confidence: 99%

Section: Hybrid Interface Treatmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

OReilly

Nordström

Kozdon

et al. 2015

Commun. Comput. Phys.

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“…The main reason to use weak boundary procedures stems from the fact that together with summation-by-parts operators they lead to provable stable schemes. For application of this technique to finite difference methods, node-centered finite volume methods, spectral domain methods and various hybrid methods see [25,42,4,30,31,36,44,48,20,39,6,22,13,24], [32,47,45,46,14,41], [18,16,19,7] and [33,34,15,37,5] respectively. In this paper we will consider a new effect of using weak boundary procedures, namely that it in many cases (all that we tried) speeds up the convergence to steady-state.…”

Section: Introductionmentioning

confidence: 99%

Weak and strong wall boundary procedures and convergence to steady-state of the Navier–Stokes equations

Nordström

Eriksson

Eliasson

2012

Journal of Computational Physics

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“…5,6,9,10,[12][13][14][15] The main reason to use weak boundary procedures (the term boundary condition refers to the continuous problem and boundary procedure is assigned to the numerical implementation of the boundary condition) together with summation-by-parts operators and the energy method is the fact that with this combination, provable stable schemes can be constructed.…”

Section: Introductionmentioning

confidence: 99%

Energy Stable High Order Finite Difference Methods for Hyperbolic Equations in Moving Coordinate Systems

Nikkar

Nordström

2013

21st AIAA Computational Fluid Dynamics Conference

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A time-dependent coordinate transformation of a constant coefficient hyperbolic equation which results in a variable coefficient problem is considered. By using the energy method, we derive well-posed boundary conditions for the continuous problem. It is shown that the number of boundary conditions depend on the coordinate transformation. By using Summation-by-Parts (SBP) operators for the space discretization and weak boundary conditions, an energy stable finite difference scheme is obtained. We also show how to construct a time-dependent penalty formulation that automatically imposes the right number of boundary conditions. Numerical calculations corroborate the stability and accuracy of the approximations.

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A hybrid method for unsteady inviscid fluid flow

Cited by 23 publications

References 28 publications

Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

Weak and strong wall boundary procedures and convergence to steady-state of the Navier–Stokes equations

Energy Stable High Order Finite Difference Methods for Hyperbolic Equations in Moving Coordinate Systems

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