Stability investigation of Runge–Kutta schemes with artificial dissipator on curvilinear grids for the Euler equations

Ganzha, Victor; Vorozhtsov, Evgenii V.

doi:10.1016/s0378-4754(01)00321-4

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Stability and Dispersion Analysis1

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2011

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“…The analysis of the stability condition given above is somehow rough and approximate. Although, Ganzha and Vorozhtsov (2001) applied the Von Neumann analysis to the fluid dynamics problem in curvilinear coordinates, the methodology is not fully appropriated; the matrices A ξ and A η not only include the elastic parameters ρ, λ and μ but also the metrics of the the coordinate transformation. Assuming a constant Jacobian matrix is physically incoherent.…”

Section: Stability and Dispersion Analysismentioning

confidence: 99%

New curvilinear scheme for elastic wave propagation in presence of curved topography

Tarrass

Giraud

Thore

2011

Geophysical Prospecting

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A B S T R A C TWe study a new curvilinear scheme for wave propagation modelling in presence of topography. The discrete scheme takes advantage of recent developments in areoacoustics. Our new scheme relies on the conventional grid coupled with optimized filters to remove numerical noise in case of strong material heterogeneity. We used non-centred stencils for free surface implementation and optimized the explicit RungeKutta scheme for the time differencing. We performed a complete theoretical stability and dispersion analysis of the discrete scheme. Finally, we illustrate the numerical accuracy of the new scheme by intensive experiments.

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Section: Stability and Dispersion Analysismentioning

confidence: 99%