Finite-volume schemes for shallow-water equations

Kurganov, Alexander

doi:10.1017/s0962492918000028

Cited by 83 publications

(53 citation statements)

References 152 publications

(339 reference statements)

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“…The coefficients {( r 1 ) k , ( r 2 ) k , ( r 3 ) k } M k=0 , as well as { α k } M k=0 are calculated via discrete Legendre transform (DLT) and inverse discrete Legendre transform (IDLT), which can be briefly described as follows. 20 • DLT: First, the Galerkin projection applied to the expansion f (…”

mentioning

confidence: 99%

Stochastic Galerkin method for cloud simulation

Chertock

Kurganov

Lukáčová-Medviďová

et al. 2019

Mathematics of Climate and Weather Forecasting

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We develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model parameters and initial or boundary conditions. The developed stochastic Galerkin method combines the space-time approximation obtained by a suitable finite volume method with a spectral-type approximation based on the generalized polynomial chaos expansion in the stochastic space. The resulting numerical scheme yields a second-order accurate approximation in both space and time and exponential convergence in the stochastic space. Our numerical results demonstrate the reliability and robustness of the stochastic Galerkin method. We also use the proposed method to study the behavior of clouds in certain perturbed scenarios, for examples, the ones leading to changes in macroscopic cloud pattern as a shift from hexagonal to rectangular structures.

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mentioning

confidence: 99%

Stochastic Galerkin method for cloud simulation

Chertock

Kurganov

Lukáčová-Medviďová

et al. 2019

Mathematics of Climate and Weather Forecasting

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“…The patch scheme could be based upon alternative microscale systems such as finite element, or finite volume methods [23,24, e.g. ], or a particle‐based method such as lattice Boltzmann [25, e.g.…”

Section: Stagger Patches Of Staggered Microcode In 2d Spacementioning

confidence: 99%

Large‐scale simulation of shallow water waves via computation only on small staggered patches

Bunder

Divahar

Kevrekidis

et al. 2020

Numerical Methods in Fluids

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A multiscale computational scheme is developed to use given small microscale simulations of complicated physical wave processes to empower macroscale system‐level predictions. By coupling small patches of simulations over unsimulated space, large savings in computational time are realizable. Here, we generalize the patch scheme to the case of wave systems on staggered grids in two‐dimensional (2D) space. Classic macroscale interpolation provides a generic coupling between patches that achieves consistency between the emergent macroscale simulation and the underlying microscale dynamics. Spectral analysis indicates that the resultant scheme empowers feasible computation of large macroscale simulations of wave systems even with complicated underlying physics. As an example of the scheme's application, we use it to simulate some simple scenarios of a given turbulent shallow water model.

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“…The shallow water equations are (as described earlier), a nonlinear hyperbolic system of PDEs. These are commonly known as very complicated systems to solve, because of the non-smooth solutions which could also contain shock and rarefaction waves, and the possible discontinuities (occurs due to discontinuous bottom topography or cross section) (Kurganov, 2018). Further, the numerical solutions could break down even for a system with smooth initial data and no discontinuities.…”

Section: Model Reduction For Non-prismatic Channelmentioning

confidence: 99%

“…Further, the numerical solutions could break down even for a system with smooth initial data and no discontinuities. Therefore, solving the shallow water equations in a stable and accurate manner, specially for a nonprismatic channel (with discontinuities) is a difficult task (Kurganov, 2018). There are well-balanced and well-developed numerical schemes available, which address these issues.…”

Section: Model Reduction For Non-prismatic Channelmentioning

confidence: 99%

Modeling and Analysis of Fluid Flow through A Non-Prismatic Open Channel with Application to Drilling

Jinasena¹,

Ghaderi²,

Sharma³

2018

MIC

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This paper presents the development and validation of a simplified dynamic model of a Venturi channel. The existing dynamic models on open channels are based on the open channel flow principles, which are the shallow water equations. Although there are analytical solutions available for steady state analysis, the numerical solution of these partial differential equations is challenging for dynamic flow conditions. There are many complete and detailed models and numerical methods available for open channel flows, however, these are usually computationally heavy. Hence they are not suitable for online monitoring and control applications, where fast estimations are needed. The orthogonal collocation method could be used to reduce the order of the model and could lead to simple solutions. The orthogonal collocation method has been used in many chemical engineering applications. Further, this has been used in prismatic open channel flow problems for control purposes, but no literature is published about its use for non-prismatic channels as per the author's knowledge. The models for non-prismatic channels have more non-linearity which is interesting to study. Therefore, the possibility of using the collocation method for determining the dynamic flow rate of a non-prismatic open channel using the fluid level measurements is investigated in this paper. The reduced order model is validated by comparing the simulated test case results with a well-developed numerical scheme. Further, a Bayesian sensitivity analysis is discussed to see the effect of parameters on the output flow rate.

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Finite-volume schemes for shallow-water equations

Cited by 83 publications

References 152 publications

Stochastic Galerkin method for cloud simulation

Stochastic Galerkin method for cloud simulation

Large‐scale simulation of shallow water waves via computation only on small staggered patches

Modeling and Analysis of Fluid Flow through A Non-Prismatic Open Channel with Application to Drilling

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