BALANCE ERRORS IN NUMERICAL SOLUTIONS OF SHALLOW WATER EQUATIONS

BALANCE ERRORS IN NUMERICAL SOLUTIONS OF SHALLOW WATER EQUATIONS

An analysis of the conservative properties of shallow water equations is presented, focused on the consistency of their numerical solution with the conservation laws of mass and momentum. Two different conservative forms are considered, solved by an implicit box scheme. Theoretical analysis support...

Full description

Bibliographic Details
Main Author:	DARIUSZ GĄSIOROWSKI
Format:	Article
Language:	English
Published:	Gdańsk University of Technology 2007-10-01
Series:	TASK Quarterly
Subjects:	shallow water equations nonlinear advection equations numerical errors conservation laws mass and momentum balance
Online Access:	https://journal.mostwiedzy.pl/TASKQuarterly/article/view/2057

Similar Items

Theoretical Time Evolution of Numerical Errors When Using Floating Point Numbers in Shallow‐Water Models
by: Tsuyoshi Yamaura, et al.
Published: (2019-10-01)

Impact of the Finite Element Mesh Structure on the Solution Accuracy of a Two-Dimensional Kinematic Wave Equation
by: Dariusz Gąsiorowski
Published: (2022-02-01)

Staggered Conservative Scheme for 2-Dimensional Shallow Water Flows
by: Novry Erwina, et al.
Published: (2020-08-01)

Traveling wave solutions for shallow water equations
by: U.M. Abdelsalam
Published: (2017-03-01)

Adaptive method for the solution of 1D and 2D advection–diffusion equations used in environmental engineering
by: Romuald Szymkiewicz, et al.
Published: (2021-11-01)

Numerical Investigation of Pollutant Transport in a Realistic Terrain with the SPH-SWE Method
by: Lirong Tian, et al.
Published: (2022-04-01)

Nonlinear sub-diffusion and nonlinear sub-diffusion dispersion equations and their proposed solutions
by: Sene Ndolane, et al.
Published: (2020-03-01)

Numerical Solution of the Advection-Diffusion Equation Using the Radial Basis Function
by: La Ode Sabran, et al.
Published: (2023-10-01)

Two efficient numerical techniques for solutions of fractional shallow water equation
by: Mohammad Izadi, et al.
Published: (2024-03-01)

Porous Shallow-Water Equations Model with Disambiguation of Multiple Solutions
by: Giada Varra, et al.
Published: (2022-10-01)

Numerical solution to nonlinear Tricomi equation using WENO schemes
by: Adrian Sescu, et al.
Published: (2010-09-01)

The mR scheme to the shallow water equation with horizontal density gradients in one and two dimensions
by: Kamel Mohamed, et al.
Published: (2023-09-01)

Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling
by: Gayaz Khakimzyanov, et al.
Published: (2019-04-01)

Weak Local Residuals as Smoothness Indicators in Adaptive Mesh Methods for Shallow Water Flows
by: Sudi Mungkasi, et al.
Published: (2020-03-01)

Approximate and numerical solution of forced nonlinear evolution equations /
by: Ong, Chee Tiong 401790, et al.
Published: (2003)

Nonlinear monotonization of the Babenko scheme for the quasi‐linear advection equation
by: T. A. Alexandrikova, et al.
Published: (2005-06-01)

Numerical Solution to Advection-Dispersion Equation with Transient Storage Zones, Considering Unsteady Flow in Irregular Cross Section Rivers
by: Maryam Barati Moghadam, et al.
Published: (2017-02-01)

Computational study of some nonlinear shallow water equations
by: Bhrawy Ali, et al.
Published: (2013-04-01)

Preserving stationary discontinuities in two-layer shallow water equations with a novel well-balanced approach
by: Majid Akbari, et al.
Published: (2023-09-01)

A second-order accurate fluid-in-cell (FLIC) method for the 2D shallow water equations with topography
by: D.M. Kelly
Published: (2017-01-01)

Numerical solutions for two nonlinear wave equations
by: Yi-feng Zhang, et al.
Published: (2012-12-01)

Numerical Solutions of the Nonlinear Dispersive Shallow Water Wave Equations Based on the Space–Time Coupled Generalized Finite Difference Scheme
by: Po-Wei Li, et al.
Published: (2023-07-01)

Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation
by: Chaudry Masood Khalique, et al.
Published: (2021-06-01)

MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM
by: Tomáš Bodnár, et al.
Published: (2021-02-01)

Numerical Solutions of Space-Fractional Advection–Diffusion–Reaction Equations
by: Valentina Anna Lia Salomoni, et al.
Published: (2021-12-01)

Different Groups of Variational Principles for Whitham-Broer-‎Kaup Equations in Shallow Water
by: Xiao-Qun Cao, et al.
Published: (2020-12-01)

Discontinuity Capture in One-Dimensional Space Using the Numerical Manifold Method with High-Order Legendre Polynomials
by: Yan Zeng, et al.
Published: (2020-12-01)

Numerical solution of unsteady state fractional advection–dispersion equation
by: Nigussie Abeye, et al.
Published: (2022-12-01)

Numerical solution of nonlinear equations /
by: Glashoff, Klaus, 1947-, et al.
Published: (1981)

Global classical solutions to equatorial shallow-water equations
by: Yue Fang, et al.
Published: (2023-09-01)

RATIONALE FOR WEAK APPROXIMATION METHOD FOR SHALLOW WATER EQUATIONS
by: N. A. Kucher, et al.
Published: (2014-11-01)

Numerical study for a class of time fractional diffusion equations using operational matrices based on Hosoya polynomial
by: Ping Zhou, et al.
Published: (2023-06-01)

AN OCEAN DEPTH-CORRECTION METHOD FOR REDUCING MODEL ERRORS IN TSUNAMI TRAVEL TIME: APPLICATION TO THE 2010 CHILE AND 2011 TOHOKU TSUNAMIS
by: Dailin Wang
Published: (2015-02-01)

The theory of approximate methods and their application to the numerical solution of singular integral equations /
by: 351717 Ivanov, V. V.
Published: (1976)

Projective Integration for Hyperbolic Shallow Water Moment Equations
by: Amrita Amrita, et al.
Published: (2022-05-01)

Homotopy Perturbation Method For Fractional Shallow Water Equations
by: Kamel Al-Khaled, et al.
Published: (2014-06-01)

Coupling Conditions for Water Waves at Forks
by: Jean–Guy Caputo, et al.
Published: (2019-03-01)

Soliton solutions, Painleve analysis and conservation laws for a nonlinear evolution equation
by: S.T.R. Rizvi, et al.
Published: (2021-04-01)

A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation
by: Hakon A. Hoel
Published: (2007-07-01)

On the use of exponential time integration methods in atmospheric models
by: Colm Clancy, et al.
Published: (2013-12-01)