WENOCLAW: A Higher Order Wave Propagation Method

Ketcheson, David I.; LeVeque, Randall J.

doi:10.1007/978-3-540-75712-2_60

Cited by 16 publications

(29 citation statements)

References 7 publications

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“…The nonlinear set of equations (2.1)-(2.3) is solved with SharpClaw, the new incarnation of WENOCLAW (Ketcheson & LeVeque 2008), in the computational domain with cells C i = (X i−1/2 , X i+1/2 ), i = 1, . .…”

Section: Numerical Simulationmentioning

confidence: 99%

Competition between kinematic and dynamic waves in floods on steep slopes

Bohorquez

2010

J. Fluid Mech.

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We present a theoretical stability analysis of the flow after the sudden release of a fixed mass of fluid on an inclined plane formally restricted to relatively long time scales, for which the kinematic regime is valid. Shallow-water equations for steep slopes with bed stress are employed to study the threshold for the onset of roll waves. An asymptotic solution for long-wave perturbations of small amplitude is found on background flows with a Froude number value of 2. Small disturbances are stable under this condition, with a linear decay rate independent of the wavelength and with a wavelength that increases linearly with time. For larger values of the Froude number it is shown that the basic flow moves at a different scale than the perturbations, and hence the wavelength of the unstable modes is characterized as a function of the plane-parallel Froude number Fr p and a measure of the local slope of the free-surface height φ by means of a multiple-scale analysis in space and time. The linear stability results obtained in the presence of small non-uniformities in the flow, φ > 0, introduce substantial differences with respect to the plane-parallel flow with φ = 0. In particular, we find that instabilities do not occur at Froude numbers Fr cr much larger than the critical value 2 of the parallel case for some wavelength ranges. These results differ from that previously reported by Lighthill & Whitham (Proc. R. Soc. A, vol. 229, 1955, pp. 281-345), because of the fundamental role that the nonparallel, time-dependent characteristics of the kinematic-wave play in the behaviour of small disturbances, which was neglected in their stability analyses. The present work concludes with supporting numerical simulations of the evolution of small disturbances, within the framework of the frictional shallow-water equations, that are superimposed on a base state which is essentially a kinematic wave, complementing the asymptotic theory relevant near the onset. The numerical simulations corroborate the cutoff in wavelength for the spectrum that stabilizes the tail of the dam-break flood.

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Section: Numerical Simulationmentioning

confidence: 99%

Competition between kinematic and dynamic waves in floods on steep slopes

Bohorquez

2010

J. Fluid Mech.

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“…The above-described phenomenon has been observed not only by using the characteristicbased reconstruction but also for the componentwise, wave-slope and transmission-based reconstruction [12]. For this reason, the comparison between the asymptotic (16) and the numerical solution for the attenuation of the infinitesimal disturbances (h, u) T can only be done in the region that is not affected by hydrodynamic instabilities, which is approximately X < 20 in the numerical simulation shown in Fig.…”

Section: Resultsmentioning

confidence: 98%

“…Left-and right-going flux differences are computed using Roe's approximate Riemann solver with entropy fix for transonic rarefactions. Both reconstruction schemes, as well as the wave-slope and transmission-based reconstruction, are implemented by default in SharpClaw, the new incarnation of WENOCLAW [12] which has been adapted here to perform the WENO2 simulations in Sect. 3.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Hydrodynamic Instabilities in Well-Balanced Finite Volume Schemes for Frictional Shallow Water Equations. The Kinematic Wave Case

Bohorquez

Rentschler

2010

J Sci Comput

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We report the developments of hydrodynamic instabilities in several wellbalanced finite volume schemes that are observed during the computation of the temporal evolution of an out-balance flow which is essentially a kinematic wave. The numerical simulations are based on the one-dimensional shallow-water equations for a uniformly sloping bed with hydraulic resistance. Subsequently, we highlight the need of low dissipative high-order well-balanced filter schemes for non-equilibrium flows with variable cut-off wavenumber to compute the out-balance flow under consideration, i.e. the kinematic wave.

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“…A simpler alternative is the method of lines, in which the spatial derivatives are discretized first, leading to a system of ODEs that can be solved by traditional methods. This is the approach taken in SharpClaw [10,9,11]. First, a non-oscillatory approximation of the solution is reconstructed from the cell averages to give high order accurate point values just to the left and right of each cell interface.…”

Section: Finite Volume Hyperbolic Pde Solversmentioning

confidence: 99%

PyClaw: Accessible, Extensible, Scalable Tools for Wave Propagation Problems

Ketcheson¹,

Mandli²,

Ahmadia³

et al. 2012

SIAM J. Sci. Comput.

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Development of scientific software involves tradeoffs between ease of use, generality, and performance. We describe the design of a general hyperbolic PDE solver that can be operated with the convenience of MATLAB yet achieves efficiency near that of hand-coded Fortran and scales to the largest supercomputers. This is achieved by using Python for most of the code while employing automatically-wrapped Fortran kernels for computationally intensive routines, and using Python bindings to interface with a parallel computing library and other numerical packages. The software described here is PyClaw, a Python-based structured grid solver for general systems of hyperbolic PDEs [18]. PyClaw provides a powerful and intuitive interface to the algorithms of the existing Fortran codes Clawpack and SharpClaw, simplifying code development and use while providing massive parallelism and scalable solvers via the PETSc library. The package is further augmented by use of PyWENO for generation of efficient high-order weighted essentially non-oscillatory reconstruction code. The simplicity, capability, and performance of this approach are demonstrated through application to example problems in shallow water flow, compressible flow and elasticity.

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WENOCLAW: A Higher Order Wave Propagation Method

Cited by 16 publications

References 7 publications

Competition between kinematic and dynamic waves in floods on steep slopes

Competition between kinematic and dynamic waves in floods on steep slopes

Hydrodynamic Instabilities in Well-Balanced Finite Volume Schemes for Frictional Shallow Water Equations. The Kinematic Wave Case

PyClaw: Accessible, Extensible, Scalable Tools for Wave Propagation Problems

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