Multi-Dimensional Semi-Lagrangian Characteristic Approach to the Shallow Water Equations by the Cip Method

Ogata, Yoichi; Yabe, Takashi

doi:10.1142/s1465876304002642

Cited by 12 publications

(25 citation statements)

References 15 publications

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“…(10) for the coordinates are in advection form. These last two equations are written in diagonal form in order to find the Riemann invariants and characteristics curves, a detailed description of this procedure can be found in (Ogata and Takashi, 2004) or (Stoker, 1992 has eigenvalues Λ given by…”

Section: Methods Of Characteristics For Sswementioning

confidence: 99%

Tree-based mesh-refinement GPU accelerated tsunami simulator for real time operation

Acuna¹,

Aoki²

2017

Preprint

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Abstract. This paper presents a fast and accurate tsunami real time operational model to compute across-ocean wide-simulations completely on GPU. The spherical shallow water equations are solved using the method of characteristics and upwind cubic-interpolation, to provide high accuracy and stability. A customized, user interactive, tree based mesh 10 refinement method is implemented based on distance from the coast and focal areas to generate a memory efficient domain with resolutions of up to 50m. Three GPU kernels, specialized and optimized (wet, wall and inundation) are developed to compute the domain block mesh. Multi-GPU is used to further speed up the computation and a weighted Hilbert space filling curve is used to produce balanced work load. Hindcasting of the 2004 Indonesia tsunami is presented to validate and compare the agreement of the arrival times and main peaks at several gauges. Inundation maps are also produced for Kamala 15 and Hambantota to validate the accuracy of our model. Test runs on three Tesla P100 cards on Tsubame 3.0 could fully simulate 10 hours in just under 10 minutes wall clock time.

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Section: Methods Of Characteristics For Sswementioning

confidence: 99%

Tree-based mesh-refinement GPU accelerated tsunami simulator for real time operation

Acuna¹,

Aoki²

2017

Preprint

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“…(4) must be solved with finite difference additionally [9]. It has already been proved in previous literatures [11,13,20] that the CIP method has extremely low dispersion error and numerical damping.…”

Section: Cip Methodsmentioning

confidence: 99%

“…Nonetheless, in semi-Lagrangian approaches, it has already been proved that correct estimations of characteristic speeds in characteristics can give correct numerical solutions even for large CFL numbers [11,26] when C satisfies Lipschitz condition, in other words, longer time step size can be taken when flows are smooth. In order to confirm the speculation, we take the other two initial conditions.…”

Section: Numerical Tests For Various Cfl Numbers In One Dimensionmentioning

confidence: 99%

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Conservative semi-Lagrangian CIP technique for the shallow water equations

Yabe

Ogata

2009

Comput Mech

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A new characteristic approach that guarantees the conservative property is proposed and is applied to the shallow water equations. CIP-CSL (Constrained Interpolation Profile/Conservative Semi-Lagrangian) interpolation is applied to the CIP method of characteristics in order to enhance the mass conservation of the numerical result. Although the characteristic formulation is originally derived from non-conservative form, present scheme achieves complete mass conservation by solving mass conservation simultaneously and reflecting conserving mass in interpolation profile. Present method has less height error compared to the CIP method of characteristics by several orders of magnitude. By the enhanced conservation property, present scheme is applicable to nonlinear problems, such as a shock problem. Furthermore, application to two dimensions including the Coriolis term is straightforward with directional splitting technique.

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“…Erbes [9] proposed a semi-Lagrangian method of characteristics (MOC) with quadratic interpolation to solve the shallow water equations with a large CFL number, but there was dispersion error produced. Ogata and Yabe [10] applied the CIP method to shallow waters combined with the MOC and showed low dispersion error and low numerical damping even with large CFL number. Toda et al [11] proposed a new scheme by adopting the Conservative Semi-Lagrangian (CSL) based on the CIP method which shows good conservation.…”

Section: Introductionmentioning

confidence: 99%

CIP Method of Characteristics for the Solution of Tide Wave Equations

Nie

2018

Advances in Mathematical Physics

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The CIP-MOC (Constrained Interpolation Profile/Method of Characteristics) is proposed to solve the tide wave equations with large time step size. The bottom topography and bottom friction, which are very important factor for the tidal wave model, are included to the equation of Riemann invariants as the source term. Numerical experiments demonstrate the good performance of the scheme. Compared to traditional semi-implicit (SI) finite difference scheme which is widely used in tidal wave simulation, CIP-MOC has better stability in simulating large gradient water surface change and has the ability to use much longer time step size under the premise of maintaining accuracy. Besides, numerical tests with reflective boundary conditions are carried out by CIP-MOC with large time step size and good results are obtained.

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Multi-Dimensional Semi-Lagrangian Characteristic Approach to the Shallow Water Equations by the Cip Method

Cited by 12 publications

References 15 publications

Tree-based mesh-refinement GPU accelerated tsunami simulator for real time operation

Tree-based mesh-refinement GPU accelerated tsunami simulator for real time operation

Conservative semi-Lagrangian CIP technique for the shallow water equations

CIP Method of Characteristics for the Solution of Tide Wave Equations

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