Higher‐order upwind leapfrog methods for multi‐dimensional acoustic equations

Kim, Cheolwan

doi:10.1002/fld.652

Cited by 8 publications

(4 citation statements)

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“…Schemes similar to (2)-(4) exist in the literature; they are the Upwind Leapfrog (UL) schemes first discussed by Iserlis for linear advection [14], and later developed by Roe [26], Tran and Scheurer [34], and Kim [18] for multidimensional wave propagation. However these schemes were neither conservative with non-uniform grids, nor based on a compact onespace-cell one-time-step computational stencil.…”

Section: Introductionmentioning

confidence: 99%

Compact Accurately Boundary-Adjusting high-REsolution Technique for fluid dynamics

Karabasov¹,

Goloviznin²

2009

Journal of Computational Physics

182

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Section: Introductionmentioning

confidence: 99%

Compact Accurately Boundary-Adjusting high-REsolution Technique for fluid dynamics

Karabasov¹,

Goloviznin²

2009

Journal of Computational Physics

182

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“…Using the same analysis as before one verifies that, as long as ∆t|k| < 2, all eigenvalues λ of the matrix in (18) fulfill |λ| = 1. This property of non-dissipativity has been the focus of [TR93,Roe98,Kim04]. They compare, for linear advection ∂ t q + c∂ x q = 0, the standard leap-frog…”

Section: Non-dissipativitymentioning

confidence: 99%

All-speed numerical methods for the Euler equations via a sequential explicit time integration

Barsukow¹

2023

Preprint

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This paper presents a new strategy to deal with the excessive diffusion that standard finite volume methods for compressible Euler equations display in the limit of low Mach number. The strategy can be understood as using centered discretizations for the acoustic part of the Euler equations and stabilizing them with a leap-frog-type ("sequential explicit") time integration, a fully explicit method. This time integration takes inspiration from time-explicit staggered grid numerical methods. In this way, advantages of staggered methods carry over to collocated methods. The paper provides a number of new collocated schemes for linear acoustic/Maxwell equations that are inspired by the Yee scheme. They are then extended to an all-speed method for the full Euler equations on Cartesian grids. By taking the opposite view and taking inspiration from collocated methods, the paper also suggests a new way of staggering the variables which increases the stability as compared to the traditional Yee scheme.

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“…Schemes similar to (2)-(4) exist in the literature; they are the Upwind Leapfrog (UL) schemes first discussed by Iserlis for linear advection (1986), and later developed by Roe (1998), Tran and Scheurer (2002), and Kim (2004) for multidimensional wave propagation. However these schemes were neither conservative, nor based on a compact one-space-cell one-time-step computational stencil.…”

Section: Comparison With Other Leapfrog Schemesmentioning

confidence: 99%