A stable and conservative method for locally adapting the design order of finite difference schemes

Eriksson, Sofia; Abbas, Qaisar; Nordström, Jan

doi:10.1016/j.jcp.2010.11.020

Cited by 21 publications

(17 citation statements)

References 26 publications

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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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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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“…Thus there is no need to use a detection algorithm to locate the regions of sharp variation apart from flux limiters that are applied for smoothing. However, the methodology may be extended to time-dependent regions, see [20]. A fourth-order Runge-Kutta method is used for the time integration.…”

Section: Methodsmentioning

confidence: 99%

“…The MUSCL scheme can be rewritten in SBP operator form with an artificial dissipation term [28] and can therefore be coupled with other schemes using SBP operators [20]. In order to enable energy estimates, the artificial dissipation must be zero at the interface.…”

Section: Hybrid Schemementioning

confidence: 99%

An intrusive hybrid method for discontinuous two-phase flow under uncertainty

2013

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An intrusive stochastic projection method for two-phase time-dependent flow subject to uncertainty is presented. Numerical experiments are carried out assuming uncertainty in the location of the physical interface separating the two phases, but the framework generalizes to uncertainty with known distribution in other input data. Uncertainty is represented through a truncated multiwavelet expansion.We assume that the discontinuous features of the solution are restricted to computational subdomains and use a high-order method for the smooth regions coupled weakly through interfaces with a robust shock capturing method for the non-smooth regions.The discretization of the non-smooth region is based on a generalization of the HLL flux, and have many properties in common with its deterministic counterpart. It is simple and robust, and captures the statistics of the shock. * Corresponding author. Address: 488 Escondido Mall, Stanford University, Stanford, CA 94305-3024, USA. Phone: +16507216565Email addresses: massperp@stanford.edu (Per Pettersson ), jops@stanford.edu (Gianluca Iaccarino), jan.nordstrom@liu.se (Jan Nordström) Preprint submitted to Computer and Fluids June 3, 2013 The discretization of the smooth region is carried out with high-order finitedifference operators satisfying a summation-by-parts property.

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“…[19] so we just state the result here as a proposition, Proposition 5.1. The interface scheme (78) is stable and conservative for…”

Section: Extending the Interface Treatmentmentioning

confidence: 99%

“…The characteristic equation (19) has double roots fors = −4 ands = 0. The solutions are κ = −1, κ = 1 (82)…”

Section: Advectionmentioning

confidence: 99%

Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains

Berg

Nordström

2012

Applied Numerical Mathematics

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In this paper we study the heat and advection equation in single and multiple domains. We discretize using a second order accurate finite difference method on Summation-By-Parts form with weak boundary and interface conditions. We derive analytic expressions for the spectrum of the continuous problem and for their corresponding discretization matrices. We show how the spectrum of the single domain operator is contained in the multi domain operator spectrum when artificial interfaces are introduced. We study the impact on the spectrum and discretization errors depending on the interface treatment and verify that the results are carried over to higher order accurate schemes.

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A stable and conservative method for locally adapting the design order of finite difference schemes

Cited by 21 publications

References 26 publications

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

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

An intrusive hybrid method for discontinuous two-phase flow under uncertainty

Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains

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