scholarly journals Numerical Simulation of Propagation and Run-Up of Long Waves in U-Shaped Bays

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 146
Author(s):  
S. R. Pudjaprasetya ◽  
Vania M. Risriani ◽  
Iryanto
Keyword(s):  
Numerical Simulation ◽  
Wave Propagation ◽  
Long Waves ◽  
Staggered Grid ◽  
Wave Focusing ◽  
Consistent Approximation ◽  
Saint Venant Equations ◽  
Wave Shoaling ◽  
Run Up ◽  
Good Agreement

Wave propagation and run-up in U-shaped channel bays are studied here in the framework of the quasi-1D Saint-Venant equations. Our approach is numerical, using the momentum conserving staggered-grid (MCS) scheme, as a consistent approximation of the Saint-Venant equations. We carried out simulations regarding wave focusing and run-ups in U-shaped bays. We obtained good agreement with the existing analytical results on several aspects: the moving shoreline, wave shoaling, and run-up heights. Our findings also confirm that the run-up height is significantly higher in the parabolic bay than on a plane beach. This assessment shows the merit of the MCS scheme in describing wave focusing and run-up in U-shaped bays. Moreover, the MCS scheme is also efficient because it is based on the quasi-1D Saint-Venant equations.

scholarly journals The Momentum Conserving Scheme Implementation for Simulating Dambreak Flow in a Channel with Various Contractions

2021 ◽  
Vol 925 (1) ◽  
pp. 012012
Author(s):  
P V Swastika ◽  
S R Pudjaprasetya
Keyword(s):  
Detrimental Effect ◽  
Point Of View ◽  
Staggered Grid ◽  
Rapid Flow ◽  
Saint Venant Equations ◽  
Grid Scheme ◽  
Life Threatening ◽  
Flow Through ◽  
Case Data ◽  
Good Agreement

Abstract Rapid flow downstream due to dambreak has a detrimental effect on the surrounding environment or, more dangerously, can be life-threatening. From a practical point of view, these flows are important to studies due to the limited dambreak real case data. This paper discusses the numerical modelling of the dambreak flow through a channel with three different contractions. Our goal here is to investigate the performance of a numerical model for solving the Saint-Venant equations using a momentum conserving staggered grid scheme (MCS). The scheme is the conservative formulation of the governing equations. Flows across channels of various widths and depths have been successfully simulated using a version of this scheme. In this work, we extend our previous work by simulating dambreak flow in a wave tank through several forms of contraction; trapezoidal and triangular. Our simulation results show good agreement with the experimental data in the literature. This assessment shows the merit of the scheme, which is suitable for dambreak flows in channels of varying width.

scholarly journals Staggered Conservative Scheme for 2-Dimensional Shallow Water Flows

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 149
Author(s):  
Novry Erwina ◽  
Didit Adytia ◽  
Sri Redjeki Pudjaprasetya ◽  
Toni Nuryaman
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Solitary Wave ◽  
Shallow Water ◽  
Threshold Value ◽  
Staggered Grid ◽  
Conservative Scheme ◽  
Shallow Water Flows ◽  
Run Up ◽  
N Wave

Simulating discontinuous phenomena such as shock waves and wave breaking during wave propagation and run-up has been a challenging task for wave modeller. This requires a robust, accurate, and efficient numerical implementation. In this paper, we propose a two-dimensional numerical model for simulating wave propagation and run-up in shallow areas. We implemented numerically the 2-dimensional Shallow Water Equations (SWE) on a staggered grid by applying the momentum conserving approximation in the advection terms. The numerical model is named MCS-2d. For simulations of wet–dry phenomena and wave run-up, a method called thin layer is used, which is essentially a calculation of the momentum deactivated in dry areas, i.e., locations where the water thickness is less than the specified threshold value. Efficiency and robustness of the scheme are demonstrated by simulations of various benchmark shallow flow tests, including those with complex bathymetry and wave run-up. The accuracy of the scheme in the calculation of the moving shoreline was validated using the analytical solutions of Thacker 1981, N-wave by Carrier et al., 2003, and solitary wave in a sloping bay by Zelt 1986. Laboratory benchmarking was performed by simulation of a solitary wave run-up on a conical island, as well as a simulation of the Monai Valley case. Here, the embedded-influxing method is used to generate an appropriate wave influx for these simulations. Simulation results were compared favorably to the analytical and experimental data. Good agreement was reached with regard to wave signals and the calculation of moving shoreline. These observations suggest that the MCS method is appropriate for simulations of varying shallow water flow.

scholarly journals Attenuation and dispersion of P-waves in porous rocks with planar fractures: Comparison of theory and numerical simulations

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. N41-N45 ◽  
Author(s):  
Gracjan Lambert ◽  
Boris Gurevich ◽  
Miroslav Brajanovski
Keyword(s):  
Numerical Simulation ◽  
Wave Propagation ◽  
Theoretical Model ◽  
Random Distribution ◽  
Constant Thickness ◽  
Porous Rocks ◽  
P Waves ◽  
Periodic Distribution ◽  
Attenuation And Dispersion ◽  
Good Agreement

To explore the validity and limitations of the theoretical model of wave propagation in porous rocks with periodic distribution of planar fractures, we perform numerical simulation using a poroelastic reflectivity algorithm. The numerical results are found to be in good agreement with the analytical model, not only for periodic fractures, but also for random distribution of constant thickness fractures.

Numerical Simulation of Wave Runup and Overtopping for Short and Long Waves Using Staggered Grid Variational Boussinesq

2020 ◽  
Vol 14 (05) ◽  
pp. 2040005
Author(s):  
Didit Adytia ◽  
Sri Redjeki Pudjaprasetya
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Water Waves ◽  
Wave Model ◽  
Long Waves ◽  
Wave Number ◽  
Staggered Grid ◽  
Type Model ◽  
Wave Runup ◽  
Conservative Scheme

In designing a numerical tool for simulating a wide variety of water waves, i.e. short to long waves, an accurate and robust wave model and numerical implementation are needed. Dispersion and nonlinearity are the two most important physical aspects that should be modeled accurately. To be applicable to simulate many coastal engineering applications, the numerical scheme should be capable of simulating wave runup and overtopping. In this paper, we extend the capability of a Boussinesq-type model called Variational Boussinesq (VB) model for simulating the runup and overtopping of water waves. To that end, the vertical layer of the fluid is modeled continuously by a linear combination of three functions. If two of these three functions have been incorporated in the previous numerical approximation called the SVB model, this paper discusses the improvement of SVB model by incorporating all the three functions. This approach improve the dispersive property of the SVB model due to its ability to simulate short waves up to kd = 20, compared to the previous model which was only up to kd = 7, where k denotes wave number and d water depth. Furthermore, the model is implemented numerically by using the staggered conservative scheme. In the new implementation, the model is switched to the non-dispersive Shallow Water Equations (SWE) when dealing with a dry area for runup and overtopping phenomena. The new implementation is tested against analytical solutions of soliton propagation and standing wave phenomenon; moreover, it is also tested against experimental data from hydrodynamic laboratories for simulating solitary wave breaking above a sloping bottom, composite beach, and in a structure for simulating overtopping phenomenon. The implementation is also tested against experimental data for simulating irregular wave propagation and runup above a fringing reef. The results of numerical simulation agree quite well with experimental data.

scholarly journals Momentum Conservative Schemes for Shallow Water Flows

2014 ◽  
Vol 4 (2) ◽  
pp. 152-165 ◽  
Author(s):  
S. R. Pudjaprasetya ◽  
I. Magdalena
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Dam Break ◽  
Staggered Grid ◽  
Conservative Scheme ◽  
Shallow Water Flows ◽  
Advection Term ◽  
Conservative Approximation ◽  
Run Up ◽  
Good Agreement

AbstractWe discuss the implementation of the finite volume method on a staggered grid to solve the full shallow water equations with a conservative approximation for the advection term. Stelling & Duinmeijer [15] noted that the advection approximation may be energy-head or momentum conservative, and if suitable which of these to implement depends upon the particular flow being considered. The momentum conservative scheme pursued here is shown to be suitable for 1D problems such as transcritical flow with a shock and dam break over a rectangular bed, and we also found that our simulation of dam break over a dry sloping bed is in good agreement with the exact solution. Further, the results obtained using the generalised momentum conservative approximation for 2D shallow water equations to simulate wave run up on a conical island are in good agreement with benchmark experimental data.

scholarly journals A Momentum-Conserving Scheme for Flow Simulation in 1D Channel with Obstacle and Contraction

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 26
Author(s):  
Putu Veri Swastika ◽  
Sri Redjeki Pudjaprasetya ◽  
Leo Hari Wiryanto ◽  
Revi Nurfathhiyah Hadiarti
Keyword(s):  
River Flow ◽  
Flow Simulation ◽  
Staggered Grid ◽  
Steady Flows ◽  
Flow Modeling ◽  
Dimensional Approach ◽  
Flow Simulations ◽  
Saint Venant Equations ◽  
Steady Solutions ◽  
Good Agreement

We consider the extension of the momentum conservative staggered-grid (MCS) scheme for flow simulation in channels with varying depth and width. The scheme is formulated using the conservative properties of the Saint-Venant equations. The proposed scheme was successful in handling various steady flows and achieved results that are in complete accordance with the analytical steady solutions. Different choices of boundary conditions have created steady solutions according to the mass and energy conservations. This assessment has served as a validation of the proposed numerical scheme. Further, in a channel with a contraction and a nonuniform bed, we simulate two cases of dam break. The simulation results show a good agreement with existing experimental data. Moreover, our scheme, that uses a quasi-1-dimensional approach, has shown some fair agreement with existing 2-dimensional numerical results. This evaluation demonstrates the merits of the MCS scheme for various flow simulations in channels of varying width and bathymetry, suitable for river flow modeling.

scholarly journals Unified wave equation and numerical simulation of mechanical wave propagation in alloy solidification

SIMULATION ◽  
2018 ◽  
Vol 95 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Rujia Wang ◽  
Shiping Wu ◽  
Wei Chen
Keyword(s):  
Numerical Simulation ◽  
Wave Propagation ◽  
Wave Equation ◽  
Constitutive Relation ◽  
Element Model ◽  
P Wave ◽  
Staggered Grid ◽  
Mechanical Wave ◽  
Propagation Law ◽  
Source Excitation

A unified wave equation of mechanical wave propagation during solidification of an alloy was established and the numerical solution of the wave equation was obtained. A three-element model (KSLS) used to describe the stress–strain constitutive relation of the alloy in the mushy zone was established by the analysis of rheological characteristics of molten melt during solidification. Based on the KSLS model, we could describe the constitutive relation of the liquid alloy, a Maxwell medium, and of the solidified alloy, an elastic medium, by the various Lame coefficients. The wave propagation during solidification was identified by a unified wave equation coming from a unified integral constitutive equation, to adapt to a variety of viscoelastic media. The wave equations could be solved succinctly by introducing a "memory factor" and the staggered grid finite difference method. The analytical results demonstrated that the unified wave equation could be perfectly applied to the numerical simulation of wave propagation during solidification. The propagation of the P-wave in a one-dimensional alloy was simulated during solidification, obtaining the propagation law of the mechanical wave: the wave with variable wavelength and amplitude propagated with attenuation during solidification; otherwise, as the source excitation force was fixed, the fluctuations caused by the mechanical wave could be more serious when the vibration was applied in the melt directly, which is more conducive to grain refinement.

scholarly journals Numerical simulation of shock wave propagation in 2-D channels with obstacles filled with chemically reacting gas suspensions

2019 ◽  
Vol 23 (Suppl. 2) ◽  
pp. 623-630 ◽  
Author(s):  
Yulia Kratova ◽  
Alexander Kashkovsky ◽  
Anton Shershnev
Keyword(s):  
Numerical Simulation ◽  
Shock Wave ◽  
Wave Propagation ◽  
Shock Wave Propagation ◽  
Test Case ◽  
Test Cases ◽  
Fortran Code ◽  
Speed Up ◽  
Chemically Reacting ◽  
Good Agreement

Modification of the serial Fortran code for solving unsteady 2-D Euler equations for the mixture of compressible gas and polydisperse particles was carried out using OpenMP technology. Modified code was verified and parallel speed-up was measured. Analysis showed that the data on parallel efficiency is in a good agreement with the Amdahls law, which gives the estimate for serial code fraction about 30%. Parallel code was used for the numerical simulation of two test-cases, namely shock wave propagation in 2-D channel with obstacles filled with reactive Al-O2 gas particle mixture and heterogeneous detonation propagation in polydisperse suspensions. For the first test-case the data on particles distribution in the flow was obtained, the existense of particle free zones inside the vortices was demonstrated and the attenuation of a shock wave was studied. In the second test, numerical simulation of detonation shock wave propagation in plain 2-D channel for the three polydisperse mixtures was carried out and data on detonation regimes was also obtained.

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