scholarly journals Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling

2020 ◽  
Author(s):  
Gayaz Khakimzyanov ◽  
Denys Dutykh ◽  
Dimitrios Mitsotakis ◽  
Nina Yu Shokina
Keyword(s):  
Finite Volume ◽  
Water Waves ◽  
Tsunami Wave ◽  
Spatial Dimension ◽  
Finite Volume Scheme ◽  
Large Solution ◽  
Monitor Function ◽  
Interpolation Procedure ◽  
Run Up ◽  
Grid Nodes

In the present article, we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with an appropriate predictor–corrector method to achieve higher resolutions. The underlying finite volume scheme is conservative, and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with large solution gradients or any other special features. No interpolation procedure is employed; thus, unnecessary solution smearing is avoided, and therefore, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according to the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves. The exact well-balanced property is proven. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up.

scholarly journals Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling

2020 ◽  
Author(s):  
Gayaz Khakimzyanov ◽  
Denys Dutykh ◽  
Dimitrios Mitsotakis ◽  
Nina Yu Shokina
Keyword(s):  
Finite Volume ◽  
Water Waves ◽  
Tsunami Wave ◽  
Spatial Dimension ◽  
Finite Volume Scheme ◽  
Large Solution ◽  
Monitor Function ◽  
Interpolation Procedure ◽  
Run Up ◽  
Grid Nodes

In the present article, we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with an appropriate predictor–corrector method to achieve higher resolutions. The underlying finite volume scheme is conservative, and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with large solution gradients or any other special features. No interpolation procedure is employed; thus, unnecessary solution smearing is avoided, and therefore, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according to the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves. The exact well-balanced property is proven. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up.

scholarly journals Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling

Geosciences ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 197 ◽  
Author(s):  
Gayaz Khakimzyanov ◽  
Denys Dutykh ◽  
Dimitrios Mitsotakis ◽  
Nina Yu. Shokina
Keyword(s):  
Finite Volume ◽  
Water Waves ◽  
Tsunami Wave ◽  
Spatial Dimension ◽  
Finite Volume Scheme ◽  
Large Solution ◽  
Monitor Function ◽  
Interpolation Procedure ◽  
Run Up ◽  
Grid Nodes

In the present article, we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with an appropriate predictor–corrector method to achieve higher resolutions. The underlying finite volume scheme is conservative, and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with large solution gradients or any other special features. No interpolation procedure is employed; thus, unnecessary solution smearing is avoided, and therefore, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according to the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves. The exact well-balanced property is proven. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up.

Two-Layer Non-Hydrostatic Scheme for Simulations of Wave Runup

2019 ◽  
Vol 13 (05n06) ◽  
pp. 1941004 ◽  
Author(s):  
M. A. Ginting ◽  
S. R. Pudjaprasetya ◽  
D. Adytia
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
Water Waves ◽  
Tsunami Wave ◽  
Harmonic Wave ◽  
Laboratory Data ◽  
Analytical Formula ◽  
Wave Simulation ◽  
Run Up ◽  
Sloping Beach

There are indisputable research supporting scientific argument that propagation of (tsunami) wave from intermediate depth towards shallower coastal area needs dispersive wave model. For tsunami wave simulation, efficiency of the numerical scheme is an important issue. In this paper, the two-layer non-hydrostatic model as developed previously in Pudjaprasetya et al. [2017] “A non-hydrostatic two-layer staggered scheme for transient waves due to anti-symmetric seabed thrust,” J. Earthquake Tsunami  11, 1–17, to study tsunami generation and propagation, is adopted. Restricting to 1+1 dimension, here, we focus on the performance of the scheme in simulating wave propagation in coastal areas, in particular predicting the run-up height. First, we conducted a simulation of harmonic wave over a sloping beach to conform the analytical shoreline motion by Carrier and Greenspan [1958] “Water waves of finite amplitude on a sloping beach,” J. Fluid Mech.  4, 97–109. The ability of the scheme in accommodating dispersion and non-linearity were shown via simulation of a solitary wave that propagates over a flat bottom. This solitary wave simulation provides an evaluation of the convergence aspect of the model. Further, several benchmark tests were conducted; a solitary wave over a sloping beach to mimic the experimental data by Synolakis [1986] “The run-up of solitary waves,” J. Fluid Mech.  185, 523–545, as well as solitary wave over a composite beach. Good agreement with laboratory data was obtained in terms of wave signal, whereas for relatively low amplitude, the solitary run-up height conforms the analytical formula. Moreover, the scheme is tested for simulating the Beji–Battjes experiment Beji, S. and Battjes, J. A. [1993] “Experimental investigation of wave propagation over a bar,” Coast. Eng.  19, 151–162. As well as wave focusing experiment by Kurnia et al. [2015] “Simulations for design and reconstruction of breaking waves in a wavetank,” Proc. ASME 2015 34th Int. Conf. Ocean, Offshore and Arctic Engineering, Newfoundland, Canada, 31 May–5 June 2015, pp. 2–7.

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

Tsunami wave run-up load reduction inside a building array

2021 ◽  
pp. 103910
Author(s):  
Joaquin P. Moris ◽  
Andrew B. Kennedy ◽  
Joannes J. Westerink
Keyword(s):  
Tsunami Wave ◽  
Load Reduction ◽  
Building Array ◽  
Run Up

scholarly journals A Hydrodynamic-Based Robust Numerical Model for Debris Hazard and Risk Assessment

2021 ◽  
Vol 13 (14) ◽  
pp. 7955
Author(s):  
Yongde Kang ◽  
Jingming Hou ◽  
Yu Tong ◽  
Baoshan Shi
Keyword(s):  
Numerical Model ◽  
Debris Flow ◽  
Finite Volume ◽  
Graphics Processing Unit ◽  
Morphological Changes ◽  
Finite Volume Scheme ◽  
Processing Unit ◽  
Algebraic Equations ◽  
Flow Process ◽  
Computing Technique

Debris flow simulations are important in practical engineering. In this study, a graphics processing unit (GPU)-based numerical model that couples hydrodynamic and morphological processes was developed to simulate debris flow, transport, and morphological changes. To accurately predict the debris flow sediment transport and sediment scouring processes, a GPU-based parallel computing technique was used to accelerate the calculation. This model was created in the framework of a Godunov-type finite volume scheme and discretized into algebraic equations by the finite volume method. The mass and momentum fluxes were computed using the Harten, Lax, and van Leer Contact (HLLC) approximate Riemann solver, and the friction source terms were calculated using the proposed splitting point-implicit method. These values were evaluated using a novel 2D edge-based MUSCL scheme. The code was programmed using C++ and CUDA, which can run on GPUs to substantially accelerate the computation. After verification, the model was applied to the simulation of the debris flow process of an idealized example. The results of the new scheme better reflect the characteristics of the discontinuity of its movement and the actual law of the evolution of erosion and deposition over time. The research results provide guidance and a reference for the in-depth study of debris flow processes and disaster prevention and mitigation.

scholarly journals Head-on collision between capillary–gravity solitary waves

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Marin Marin ◽  
M. M. Bhatti
Keyword(s):  
Surface Tension ◽  
Solitary Waves ◽  
Water Waves ◽  
Free Parameter ◽  
Order Approximation ◽  
Third Order ◽  
Boussinesq Model ◽  
Run Up ◽  
Physical Features ◽  
Third Order Approximation

AbstractThe present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is suitable for both shallow and deep water waves. We have considered the surface tension effects. To examine the asymptotic behavior, we employed the Poincaré–Lighthill–Kuo method. The resulting series solutions are given up to third-order approximation. The physical features are discussed for wave speed, head-on collision profile, maximum run-up, distortion profile, the velocity at the bottom, and phase shift profile, etc. A comparison is also given as a particular case in our study. According to the results, it is noticed that the free parameter and the surface tension tend to decline the solitary-wave profile significantly. However, the maximum run-up amplitude was affected in great measure due to the surface tension and the free parameter.

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