scholarly journals Pemodelan Propagasi Gelombang pada Linear Shallow Water Equations Menggunakan Metode Spectral

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
Setyo Nugroho ◽  
Mohamad Riyadi
Keyword(s):  
Wave Propagation ◽  
Shallow Water ◽  
Spectral Methods ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Spatial Domain ◽  
Initial Condition ◽  
Simulation Results ◽  
Propagation Of Waves

ABSTRACT In this paper , the propagation of waves with an initial condition on the foundation are varied( varying bottom ) simulated by the model Linear Shallow Water Equations ( LSWE ) 1D . 1D LSWE solution with an initial condition was approached with numerical solutions , which use spectral methods . To reduce waves so as not to repeat back to the spatial domain need to be defined damping zone. The simulation results showed that the more superficial level it will increase the amplitude of the wave . Keywords : Wave Propagation , LSWE ID , Varying Bottom , MetodeSspectral , Damping Zone

Models of non-Boussinesq lock-exchange flow

2011 ◽  
Vol 675 ◽  
pp. 1-26 ◽  
Author(s):  
R. ROTUNNO ◽  
J. B. KLEMP ◽  
G. H. BRYAN ◽  
D. J. MURAKI
Keyword(s):  
Free Boundary ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Water System ◽  
Analytic Solutions ◽  
Analytical Models ◽  
Navier Stokes ◽  
Exchange Flow

Nearly all analytical models of lock-exchange flow are based on the shallow-water approximation. Since the latter approximation fails at the leading edges of the mutually intruding fluids of lock-exchange flow, solutions to the shallow-water equations can be obtained only through the specification of front conditions. In the present paper, analytic solutions to the shallow-water equations for non-Boussinesq lock-exchange flow are given for front conditions deriving from free-boundary arguments. Analytic solutions are also derived for other proposed front conditions – conditions which appear to the shallow-water system as forced boundary conditions. Both solutions to the shallow-water equations are compared with the numerical solutions of the Navier–Stokes equations and a mixture of successes and failures is recorded. The apparent success of some aspects of the forced solutions of the shallow-water equations, together with the fact that in a real fluid the density interface is a free boundary, shows the need for an improved theory of lock-exchange flow taking into account non-hydrostatic effects for density interfaces intersecting rigid boundaries.

scholarly journals Weak Local Residuals as Smoothness Indicators in Adaptive Mesh Methods for Shallow Water Flows

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 345
Author(s):  
Sudi Mungkasi ◽  
Stephen Gwyn Roberts
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Adaptive Mesh ◽  
Finite Volume Methods ◽  
Water Type ◽  
Two Dimensional ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Smoothness Indicators

This paper proposes some formulations of weak local residuals of shallow-water-type equations, namely, one-, one-and-a-half-, and two-dimensional shallow water equations. Smooth parts of numerical solutions have small absolute values of weak local residuals. Rougher parts of numerical solutions have larger absolute values of weak local residuals. This behaviour enables the weak local residuals to detect parts of numerical solutions which are smooth and rough (non-smooth). Weak local residuals that we formulate are implemented successfully as refinement or coarsening indicators for adaptive mesh finite volume methods used to solve shallow water equations.

Maximum power from a turbine farm in shallow water

2013 ◽  
Vol 714 ◽  
pp. 634-643 ◽  
Author(s):  
Chris Garrett ◽  
Patrick Cummins
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Momentum Equation ◽  
Basic Flow ◽  
Maximum Power ◽  
Two Dimensional ◽  
Dominant Term ◽  
Tidal Flows ◽  
Linear Friction

AbstractThe maximum power that can be obtained from a confined array of turbines in steady or tidal flows is considered using the two-dimensional shallow-water equations and representing the turbine farm by a uniform local increase in friction within a circle. Analytical results supported by dimensional reasoning and numerical solutions show that the maximum power depends on the dominant term in the momentum equation for flows perturbed on the scale of the farm. If friction dominates in the basic flow, the maximum power is a fraction (half for linear friction and 0.75 for quadratic friction) of the dissipation within the circle in the undisturbed state; if the advective terms dominate, the maximum power is a fraction of the undisturbed kinetic energy flux into the front of the turbine farm; if the acceleration dominates, the maximum power is similar to that for the linear frictional case, but with the friction coefficient replaced by twice the tidal frequency.

Numerical entropy production as smoothness indicator for shallow water equations

2020 ◽  
Vol 61 ◽  
pp. 398-415
Author(s):  
Sudi Mungkasi ◽  
Stephen Gwyn Roberts
Keyword(s):  
Shallow Water ◽  
Entropy Production ◽  
Shallow Water Equations ◽  
Alternative Scheme ◽  
One Dimensional ◽  
Different Dimensions ◽  
Smoothness Indicator ◽  
Simulation Results ◽  
Numerical Entropy ◽  
Adaptive Numerical Method

The numerical entropy production (NEP) for shallow water equations (SWE) is discussed and implemented as a smoothness indicator. We consider SWE in three different dimensions, namely, one-dimensional, one-and-a-half-dimensional, and two-dimensional SWE. An existing numerical entropy scheme is reviewed and an alternative scheme is provided. We prove the properties of these two numerical entropy schemes relating to the entropy steady state and consistency with the entropy equality on smooth regions. Simulation results show that both schemes produce NEP with the same behaviour for detecting discontinuities of solutions and perform similarly as smoothness indicators. An implementation of the NEP for an adaptive numerical method is also demonstrated. doi:10.1017/S1446181119000154

scholarly journals Simulation of Ocean Circulation of Dongsha Water Using Non-Hydrostatic Shallow-Water Model

Water ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2832 ◽  
Author(s):  
Shin-Jye Liang ◽  
Chih-Chieh Young ◽  
Chi Dai ◽  
Nan-Jing Wu ◽  
Tai-Wen Hsu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Free Surface ◽  
Hydrostatic Pressure ◽  
Velocity Field ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Shallow Water Model

A two-dimensional non-hydrostatic shallow-water model for weakly dispersive waves is developed using the least-squares finite-element method. The model is based on the depth-averaged, nonlinear and non-hydrostatic shallow-water equations. The non-hydrostatic shallow-water equations are solved with the semi-implicit (predictor-corrector) method and least-squares finite-element method. In the predictor step, hydrostatic pressure at the previous step is used as an initial guess and an intermediate velocity field is calculated. In the corrector step, a Poisson equation for the non-hydrostatic pressure is solved and the final velocity and free-surface elevation is corrected for the new time step. The non-hydrostatic shallow-water model is verified and applied to both wave and flow driven fluid flows, including solitary wave propagation in a channel, progressive sinusoidal waves propagation over a submerged bar, von Karmann vortex street, and ocean circulations of Dongsha Atolls. It is found hydrostatic shallow-water model is efficient and accurate for shallow water flows. Non-hydrostatic shallow-water model requires 1.5 to 3.0 more cpu time than hydrostatic shallow-water model for the same simulation. Model simulations reveal that non-hydrostatic pressure gradients could affect the velocity field and free-surface significantly in case where nonlinearity and dispersion are important during the course of wave propagation.

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