Modeling of uncertainty for flood wave propagation induced by variations in initial and boundary conditions using expectation operator on explicit numerical solutions

2017 ◽  
Vol 113 (9) ◽  
pp. 1447-1465 ◽  
Author(s):  
Shiang-Jen Wu ◽  
Chih-Tsung Hsu
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Flood Wave ◽  
Initial And Boundary Conditions

scholarly journals Modelling of Flood Wave Propagation with Wet-dry Front by One-dimensional Diffusive Wave Equation

2014 ◽  
Vol 61 (3-4) ◽  
pp. 111-125 ◽  
Author(s):  
Dariusz Gąsiorowski
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Numerical Solutions ◽  
Numerical Algorithms ◽  
Finite Volume Methods ◽  
Flood Wave ◽  
One Dimensional ◽  
Benchmark Solution ◽  
The One ◽  
Water Depths

Abstract A full dynamic model in the form of the shallow water equations (SWE) is often useful for reproducing the unsteady flow in open channels, as well as over a floodplain. However, most of the numerical algorithms applied to the solution of the SWE fail when flood wave propagation over an initially dry area is simulated. The main problems are related to the very small or negative values of water depths occurring in the vicinity of a moving wet-dry front, which lead to instability in numerical solutions. To overcome these difficulties, a simplified model in the form of a non-linear diffusive wave equation (DWE) can be used. The diffusive wave approach requires numerical algorithms that are much simpler, and consequently, the computational process is more effective than in the case of the SWE. In this paper, the numerical solution of the one-dimensional DWE based on the modified finite element method is verified in terms of accuracy. The resulting solutions of the DWE are compared with the corresponding benchmark solution of the one-dimensional SWE obtained by means of the finite volume methods. The results of numerical experiments show that the algorithm applied is capable of reproducing the reference solution with satisfactory accuracy even for a rapidly varied wave over a dry bottom.

scholarly journals Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Bashar Zogheib ◽  
Emran Tohidi ◽  
Stanford Shateyi
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Krylov Subspace ◽  
Numerical Solutions ◽  
Dirichlet Boundary Conditions ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Collocation Points ◽  
Linear Algebraic Equations ◽  
Initial And Boundary Conditions

A numerical approach is proposed for solving multidimensional parabolic diffusion and hyperbolic wave equations subject to the appropriate initial and boundary conditions. The considered numerical solutions of the these equations are considered as linear combinations of the shifted Bernoulli polynomials with unknown coefficients. By collocating the main equations together with the initial and boundary conditions at some special points (i.e., CGL collocation points), equations will be transformed into the associated systems of linear algebraic equations which can be solved by robust Krylov subspace iterative methods such as GMRES. Operational matrices of differentiation are implemented for speeding up the operations. In both of the one-dimensional and two-dimensional diffusion and wave equations, the geometrical distributions of the collocation points are depicted for clarity of presentation. Several numerical examples are provided to show the efficiency and spectral (exponential) accuracy of the proposed method.

DETERMINISTIC APPROACH TO WATERSHED MODELING

1971 ◽  
Vol 2 (3) ◽  
pp. 146-166 ◽  
Author(s):  
DAVID A. WOOLHISER
Keyword(s):  
Boundary Conditions ◽  
Watershed Modeling ◽  
Deterministic Approach ◽  
Mass Energy ◽  
Deterministic Models ◽  
Conservation Of Mass ◽  
Hydrologic Process ◽  
Theoretical Structure ◽  
Physically Based ◽  
Initial And Boundary Conditions

Physically-based, deterministic models, are considered in this paper. Physically-based, in that the models have a theoretical structure based primarily on the laws of conservation of mass, energy, or momentum; deterministic in the sense that when initial and boundary conditions and inputs are specified, the output is known with certainty. This type of model attempts to describe the structure of a particular hydrologic process and is therefore helpful in predicting what will happen when some change occurs in the system.

Dam-Breach Flood Wave Propagation Using Dimensionless Parameters

2003 ◽  
Vol 129 (10) ◽  
pp. 777-782 ◽  
Author(s):  
Victor M. Ponce ◽  
Ahmad Taher-shamsi ◽  
Ampar V. Shetty
Keyword(s):  
Wave Propagation ◽  
Flood Wave ◽  
Dam Breach ◽  
Dimensionless Parameters
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