A stable and conservative high order multi-block method for the compressible Navier–Stokes equations

Nordström, Jan; Gong, Junbo; Weide, Edwin van der; Svärd, Magnus

doi:10.1016/j.jcp.2009.09.005

Cited by 125 publications

(104 citation statements)

References 27 publications

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“…More details on this productive and well tested technique is given below. For a read-up, see [3], [11], [13], [14], [20], [19], [21], [15], [2], [5]. A recipe for constructing a stable and convergent scheme when using the SBP-SAT technique is to choose the so called penalty parameters such that an energy-estimate is obtained.…”

Section: Recipe For Constructing a Schemementioning

confidence: 99%

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Linear and Nonlinear Boundary Conditions for Wave Propagation Problems

Nordström

2013

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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We discuss linear and nonlinear boundary conditions for wave propagation problems. The concepts of well-posedness and stability are discussed by considering a specific example of a boundary condition occurring in the modeling of earthquakes. That boundary condition can be formulated in a linear and nonlinear way and implemented in a characteristic and non-characteristic way. These differences are discussed and the implications and difficulties are pointed out. Numerical simulations that illustrate the theoretical discussion are presented together with an application that show that the methodology can be used for practical problems.

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Section: Recipe For Constructing a Schemementioning

confidence: 99%

“…More details on the weak imposition of boundary and interface conditions using the SAT technique will be given below. For a read-up on this technique see [3], [11], [13], [14], [20], [19], [21], [15]. By multiplying (17) from the left with U T (P ⊗ I) we obtain…”

Section: Sbp Operators and Weak Non Characteristic Boundary Conditionsmentioning

confidence: 99%

Linear and Nonlinear Boundary Conditions for Wave Propagation Problems

Nordström

2013

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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“…Finding analytically the inverse transformation is in general a very difficult problem but that is not our interest here. We shall use the Laplace transform to determine the spectrum of (1). Assume that g 1 = g 2 = 0 and take the Laplace transform of (1).…”

Section: Continuous Casementioning

confidence: 99%

“…The subdomains need to be coupled in a way that preserves both the stability and accuracy of the computational scheme. A proof of stability and conservation for a multiblock method for the compressible Navier-Stokes equations was shown recently in [1]. They used a finite difference method on Summation-By-Parts (SBP) form with the Simultaneous Approximation Term (SAT) technique to impose the boundary and interface conditions weakly.…”

Section: Introductionmentioning

confidence: 99%

“…They used a finite difference method on Summation-By-Parts (SBP) form with the Simultaneous Approximation Term (SAT) technique to impose the boundary and interface conditions weakly. The SBP and SAT method has been used for many applications in fluid dynamics since it has the benefit of being provable energy stable when the correct boundary and interface conditions are imposed for the PDE [1,2,3,4,5,6].…”

Section: Introductionmentioning

confidence: 99%

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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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An improved parallel compact scheme for domain‐decoupled simulation of turbulence

Fang

Gao

Moulinec

et al. 2019

Numerical Methods in Fluids

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Summary An improved domain‐decoupled compact scheme for first and second spatial derivatives is proposed for domain‐decomposition‐based parallel computational fluid dynamics. The method improves the accuracy of previously developed decoupled schemes and preserves the accuracy and bandwidth properties of fully coupled compact schemes, even for a very large degree of parallelism, and enables the Navier‐Stokes equations to be solved independently on each processor. The scheme is analysed using Fourier analysis and error analysis, and tested on one‐dimensional wave‐packet propagation, a two‐dimensional vortex convection problem, and in the direct numerical simulation of the three‐dimensional Taylor‐Green vortex problem and turbulent channel flow. Our results demonstrate the scheme's effectiveness in performing direct numerical simulation of turbulence in terms of accuracy and scalability.

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A stable and conservative high order multi-block method for the compressible Navier–Stokes equations

Cited by 125 publications

References 27 publications

Linear and Nonlinear Boundary Conditions for Wave Propagation Problems

Linear and Nonlinear Boundary Conditions for Wave Propagation Problems

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

An improved parallel compact scheme for domain‐decoupled simulation of turbulence

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