scholarly journals AN EFFICIENT AND ROBUST GPGPU-BASED SHALLOW WATER MODEL

2020 ◽  
pp. 47
Author(s):  
Fatima-zahra Mihami ◽  
Volker Roeber
Keyword(s):  
Numerical Solution ◽  
Shallow Water ◽  
Computational Cost ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Water Model ◽  
Staggered Grid ◽  
Finite Volume Scheme ◽  
Flow Solver ◽  
Riemann Solvers

We present an efficient and robust numerical model for the solution of the Shallow Water Equations with the objective to develop the numerical foundation for an advanced free surface flow solver. The numerical solution is based on an explicit Finite Volume scheme on a staggered grid to ensure the conservation of mass and momentum across flow discontinuities and wet-dry transitions. This leads to an accurate numerical solution at low computational cost without the need for Riemann solvers. The efficiency of the lean numerical structure is further optimized through a CUDA-GPU implementation.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/xMnK_r7Tj1Q

scholarly journals Congested shallow water model: roof modeling in free surface flow

2018 ◽  
Vol 52 (5) ◽  
pp. 1679-1707 ◽  
Author(s):  
Edwige Godlewski ◽  
Martin Parisot ◽  
Jacques Sainte-Marie ◽  
Fabien Wahl
Keyword(s):  
Shallow Water ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Hyperbolic Equations ◽  
Mechanical Energy ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Water Model ◽  
Shallow Water Model ◽  
Time Step

We are interested in the modeling and the numerical approximation of flows in the presence of a roof, for example flows in sewers or under an ice floe. A shallow water model with a supplementary congestion constraint describing the roof is derived from the Navier-Stokes equations. The congestion constraint is a challenging problem for the numerical resolution of hyperbolic equations. To overcome this difficulty, we follow a pseudo-compressibility relaxation approach. Eventually, a numerical scheme based on a finite volume method is proposed. The well-balanced property and the dissipation of the mechanical energy, acting as a mathematical entropy, are ensured under a non-restrictive condition on the time step in spite of the large celerity of the potential waves in the congested areas. Simulations in one dimension for transcritical steady flow are carried out and numerical solutions are compared to several analytical (stationary and non-stationary) solutions for validation.

scholarly journals Topography-based local spherical Voronoi grid refinement on classical and moist shallow-water finite-volume models

2021 ◽  
Vol 14 (11) ◽  
pp. 6919-6944
Author(s):  
Luan F. Santos ◽  
Pedro S. Peixoto
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Voronoi Tessellation ◽  
Computational Cost ◽  
Water Model ◽  
Small Scale ◽  
Finite Volume Scheme ◽  
Local Refinement ◽  
The Andes ◽  
Smooth Transitions

Abstract. Locally refined grids for global atmospheric models are attractive since they are expected to provide an alternative to solve local phenomena without the requirement of a global high-resolution uniform grid, whose computational cost may be prohibitive. Spherical centroidal Voronoi tessellation (SCVT), as used in the atmospheric Model for Prediction Across Scales (MPAS), allows a flexible way to build and work with local refinement. In addition, the Andes Range plays a key role in the South American weather, but it is hard to capture its fine-structure dynamics in global models. This paper describes how to generate SCVT grids that are locally refined in South America and that also capture the sharp topography of the Andes Range by defining a density function based on topography and smoothing techniques. We investigate the use of the mimetic finite-volume scheme employed in the MPAS dynamical core on this grid considering the nonlinear classic and moist shallow-water equations on the sphere. We show that the local refinement, even with very smooth transitions from different resolutions, generates spurious numerical inertia–gravity waves that may even numerically destabilize the model. In the moist shallow-water model, wherein physical processes such as precipitation and cloud formation are included, our results show that the local refinement may generate spurious rain that is not observed in uniform-resolution SCVT grids. Fortunately, the spurious waves originate from small-scale grid-related numerical errors and can therefore be mitigated using fourth-order hyperdiffusion. We exploit a grid geometry-based hyperdiffusion that is able to stabilize spurious waves and has very little impact on the total energy conservation. We show that, in some cases, the clouds are better represented in a variable-resolution grid when compared to a respective uniform-resolution grid with the same number of cells, while in other cases, grid effects can affect the cloud and rain representation.

scholarly journals Topography based local spherical Voronoi grid refinement on classical and moist shallow-water finite volume models

2021 ◽  
Author(s):  
Luan F. Santos ◽  
Pedro S. Peixoto
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Computational Cost ◽  
Water Model ◽  
Uniform Grid ◽  
Small Scale ◽  
Finite Volume Scheme ◽  
Local Refinement ◽  
The Andes ◽  
Smooth Transitions

Abstract. Locally refined grids for global atmospheric models are attractive since they are expected to provide an alternative to solve local phenomena without the requirement of a global high-resolution uniform grid, whose computational cost may be prohibitive. The Spherical Centroidal Voronoi Tesselations (SCVT), as used in the atmospheric Model for Prediction Across Scales (MPAS), allows a flexible way to build and work with local refinement. Alongside, the Andes Range plays a key role in the South American weather, but it is hard to capture its fine structure dynamics in global models. This paper describes how to generate SCVT grids that are locally refined in South America and that also capture the sharp topography of the Andes Range by defining a density function based on topography and smoothing techniques. We investigate the use of the mimetic finite volume scheme employed in the MPAS dynamical core on this grid considering the non-linear classic and moist shallow-water equations on the sphere. We show that the local refinement, even with very smooth transitions from different resolutions, generates spurious numerical inertia-gravity waves that may even numerically de-stabilize the model. In the moist shallow-water model, where physical processes such as precipitation and cloud formation are included, our results show that the local refinement may generate spurious rain that is not observed in uniform resolution SCVT grids. Fortunately, the spurious waves originate from small-scale grid-related numerical errors and therefore can be mitigated using small amounts of numerical diffusion. We show that, in some cases, the clouds are better represented in a variable resolution grid when compared to a respective uniform resolution grid with the same number of cells, while in other cases, grid effects can deteriorate the cloud and rain representation.

A coupled FE model for the joint resolution of the shallow water and the groundwater flow equations

2014 ◽  
Vol 24 (7) ◽  
pp. 1553-1569 ◽  
Author(s):  
H.G. Rábade ◽  
P. Vellando ◽  
F. Padilla ◽  
R. Juncosa
Keyword(s):  
Groundwater Flow ◽  
Shallow Water ◽  
Free Surface Flow ◽  
Element Model ◽  
Surface Flow ◽  
Fe Model ◽  
Content Type ◽  
Flow Equations ◽  
Natural Watersheds ◽  
Joint Resolution

Purpose – A new coupled finite element model has been developed for the joint resolution of both the shallow water equations, that governs the free surface flow, and the groundwater flow equation that governs the motion of water through a porous media. The paper aims to discuss these issues. Design/methodology/approach – The model is based upon two different modules (surface and ground water) previously developed by the authors, that have been validated separately. Findings – The newly developed software allows for the assessment of the fluid flow in natural watersheds taking into account both the surface and the underground flow in the way it really takes place in nature. Originality/value – The main achievement of this work has dealt with the coupling of both models, allowing for a proper moving interface treatment that simulates the actual interaction that takes place between surface and groundwater in natural watersheds.

A layer-integrated approach for shallow water free-surface flow computation

2007 ◽  
Vol 24 (12) ◽  
pp. 1699-1722
Author(s):  
Meng-Chi Hung ◽  
Te-Yung Hsieh ◽  
Tung-Lin Tsai ◽  
Jinn-Chuang Yang
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Free Surface Flow ◽  
Integrated Approach ◽  
Surface Flow ◽  
Flow Computation

scholarly journals A Well-balanced Finite Volume Scheme for Shallow Water Equations with Porosity: Application to Modelling Flow through Rigid Vegetation

2018 ◽  
Vol 40 ◽  
pp. 05032
Author(s):  
Minh H. Le ◽  
Virgile Dubos ◽  
Marina Oukacine ◽  
Nicole Goutal
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Simple Wave ◽  
Water Model ◽  
Strong Interactions ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Rigid Vegetation ◽  
Vertical Cylinders

Strong interactions exist between flow dynamics and vegetation in open-channel. Depth-averaged shallow water equations can be used for such a study. However, explicit representation of vegetation can lead to very high resolution of the mesh since the vegetation is often modelled as vertical cylinders. Our work aims to study the ability of a single porosity-based shallow water model for these applications. More attention on flux and source terms discretizations are required in order to archive the well-balancing and shock capturing properties. We present a new Godunov-type finite volume scheme based on a simple-wave approximation and compare it with some other methods in the literature. A first application with experimental data was performed.

Surface Ship Total Resistance Prediction Based on a Nonlinear Free Surface Potential Flow Solver and a Reynolds-Averaged Navier-Stokes Viscous Correction

2007 ◽  
Vol 51 (01) ◽  
pp. 47-64
Author(s):  
James C. Huan ◽  
Thomas T. Huang
Keyword(s):  
Free Surface ◽  
Surface Potential ◽  
Potential Flow ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Navier Stokes ◽  
Total Resistance ◽  
Flow Solver ◽  
Resistance Prediction ◽  
Nonlinear Free Surface

A fast turnaround and an accurate computational fluid dynamics (CFD) approach for ship total resistance prediction is developed. The approach consists of a nonlinear free surface potential flow solver (PShip code) with a wet-or-dry transom stern model, and a Reynolds-averaged Navier-Stokes (RANS) equation solver that solves viscous free surface flow with a prescribed free surface given from the PShip. The prescribed free surface RANS predicts a viscous correction to the pressure resistance (viscous form) and viscous flow field around the hull. The viscous free surface flow solved this way avoids the time-consuming RANS iterations to resolve the free surface profile. The method, however, requires employing a flow characteristic-based nonreflecting boundary condition at the free surface. The approach can predict the components of ship resistance, the associated wave profile around the hull, and the sinkage and trim of the ship. Validation of the approach is presented with Wigley, Series 60 (CB = 0.6), and NSWCCD Model 5415 hulls. An overall accuracy of ±2% for ship total resistance prediction is achieved. The approach is applied to evaluating the effects of a stern flap on a DD 968 model on ship performance. An empirical viscous form resistance formula is also devised for a quick ship total resistance estimate.

A Numerical Shallow Water Model Based on the Non-Orthogonal Curvilinear Grids

2006 ◽  
Author(s):  
Chaofeng Tong ◽  
Yanqiu Meng
Keyword(s):  
Shallow Water ◽  
Curvilinear Coordinates ◽  
Water Model ◽  
Staggered Grid ◽  
Shallow Water Model ◽  
Governing Equations ◽  
Cartesian Coordinates ◽  
Independent Variables ◽  
Discrete Equations ◽  
Curvilinear Grids

According to the transformation relationships between the Cartesian coordinates and the general curvilinear coordinates, the governing equations of the model are derived as the forms in the general curvilinear coordinates from those in the Cartesian coordinates. In the model, the contravariant velocities are adopted as the independent variables in non-orthogonal grids. The momentum equations keep strongly conservative forms and the boundary conditions can be given easily. The model used a staggered grid arrangement. The discrete equations are solved using the SIMPLIC algorithms. The numerical model has been validated against the bifurcated flow of which the diversion angle is 30 degree. Compared with the measured values, the numerical shallow water model is shown to be capable of simulating the water domains with irregular boundaries.

On the necessity of non-hydrostatic pressure models for free surface flow over complex topography

2020 ◽  
Author(s):  
Isabel Echeverribar ◽  
Pilar Brufau ◽  
Pilar García-Navarro
Keyword(s):  
Free Surface ◽  
Hydrostatic Pressure ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Finite Volume Scheme ◽  
Complex Topography ◽  
Source Terms ◽  
Pressure Correction ◽  
Wide Range

<p><span><strong>There is a wide range of geophysical flows, such as flow in open channels and rivers, tsunami and flood modeling, that can be mathematically represented by the non-linear shallow water 1D equations involving hydrostatic pressure assumptions as an approximation of the Navier Stokes equations. In this context, special attention must be paid to bottom source terms integration and numerical corrections when dealing with wet/dry fronts or strong slopes in order to obtain physically-based solutions (Murillo and García-Navarro, 2010) in complex and realistic cases with irregular topography. However, although these numerical corrections have been developed in recent years achieving not only more robust models but also more accurate results, they still might find a limit when dealing with specific scenarios where vertical information or disspersive effects become crucial. This work presents a 1D shallow water model that introduces vertical information by means of a non-hydrostatic pressure correction when necessary. In particular, the pressure correction method (Hirsch, 2007) is applied to a 1D finite volume scheme for a rectification of the velocity field in free surface scenarios. It is solved by means of an implicit scheme, whereas the depth-integrated shallow water equations are solved using an explicit scheme. It is worth highlighting that it preserves all the advantages and numerical fixes aforementioned for the pure shallow water system. Computations with and without non-hydrostatic corrections are compared for the same cases to test the validity of the conventional hydrostatic pressure assumption at some scenarios involving complex topography.</strong></span></p><p><span>[1] J. Murillo and P. Garcia-Navarro, Weak solutions for partial differential equations with source terms: application to the shallow water equations, Journal of Computational Physics, vol. 229, iss. 11, pp. 4327-4368, 2010.</span></p><p><span>[2] C. Hirsch, Numerical Computation of Internal and External flows: The fundamentals of Computational Fluid Dynamics, Butterworth-Heinemann, 2007.</span></p>

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