scholarly journals BORE INCEPTION AND PROPAGATION BY THE NONLINEAR WAVE THEORY

1964 ◽  
Vol 1 (9) ◽  
pp. 5
Author(s):  
Michael Amein
Keyword(s):  
Experimental Data ◽  
Finite Difference ◽  
Iterative Method ◽  
Difference Scheme ◽  
Nonlinear Theory ◽  
Laboratory Experiments ◽  
Method Of Characteristics ◽  
Wave Theory ◽  
Shallow Water Theory ◽  
Nonlinear Shallow Water Theory

The integration of the equations of the nonlinear shallow-water theory by a finite difference scheme based on the method of characteristics is programmed for digital computers. In the program, the equations of the bore propagation are coupled to the equations of the nonlinear theory, and thus a procedure for predicting the motion of the entire wave, including the bore, is established. Waves of irregular shape and experimental data are treated by an iterative method. Laboratory experiments on the inception and propagation of bores also are presented.

scholarly journals An unconditionally stable implicit difference scheme for 2D porous medium equations using four-point NEGMSOR iterative method

2018 ◽  
Vol 20 ◽  
pp. 02004
Author(s):  
Chew Jackel Vui Lung ◽  
Jumat Sulaiman
Keyword(s):  
Porous Medium ◽  
Finite Difference ◽  
Iterative Method ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Nonlinear Approximation ◽  
Solution Vector ◽  
Implicit Finite Difference Scheme ◽  
Porous Medium Equations ◽  
Implicit Finite Difference

In this paper, a numerical method has been proposed for solving several two-dimensional porous medium equations (2D PME). The method combines Newton and Explicit Group MSOR (EGMSOR) iterative method namely four-point NEGMSOR. Throughout this paper, an initialboundary value problem of 2D PME is discretized by using the implicit finite difference scheme in order to form a nonlinear approximation equation. By taking a fixed number of grid points in a solution domain, the formulated nonlinear approximation equation produces a large nonlinear system which is solved using the Newton iterative method. The solution vector of the sparse linearized system is then computed iteratively by the application of the four-point EGMSOR method. For the numerical experiments, three examples of 2D PME are used to illustrate the efficiency of the NEGMSOR. The numerical result reveals that the NEGMSOR has a better efficiency in terms of number of iterations, computation time and maximum absolute error compared to the tested NGS, NEG and NEGSOR iterative methods. The stability analysis of the implicit finite difference scheme used on 2D PME is also provided.

scholarly journals Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Andang Sunarto ◽  
Praveen Agarwal ◽  
Jumat Sulaiman ◽  
Jackel Vui Lung Chew ◽  
Elayaraja Aruchunan
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Iterative Method ◽  
Difference Scheme ◽  
Fractional Differential Equation ◽  
Relaxation Method ◽  
Mathematical Physics ◽  
One Dimensional ◽  
Fractional Differential ◽  
Preconditioned Iterative

AbstractThis paper will solve one of the fractional mathematical physics models, a one-dimensional time-fractional differential equation, by utilizing the second-order quarter-sweep finite-difference scheme and the preconditioned accelerated over-relaxation method. The proposed numerical method offers an efficient solution to the time-fractional differential equation by applying the computational complexity reduction approach by the quarter-sweep technique. The finite-difference approximation equation will be formulated based on the Caputo’s time-fractional derivative and quarter-sweep central difference in space. The developed approximation equation generates a linear system on a large scale and has sparse coefficients. With the quarter-sweep technique and the preconditioned iterative method, computing the time-fractional differential equation solutions can be more efficient in terms of the number of iterations and computation time. The quarter-sweep computes a quarter of the total mesh points using the preconditioned iterative method while maintaining the solutions’ accuracy. A numerical example will demonstrate the efficiency of the proposed quarter-sweep preconditioned accelerated over-relaxation method against the half-sweep preconditioned accelerated over-relaxation, and the full-sweep preconditioned accelerated over-relaxation methods. The numerical finding showed that the quarter-sweep finite difference scheme and preconditioned accelerated over-relaxation method can serve as an efficient numerical method to solve fractional differential equations.

Runup of long waves on composite coastal slopes: numerical simulations and experiment

2020 ◽  
Author(s):  
Ira Didenkulova ◽  
Andrey Kurkin ◽  
Artem Rodin ◽  
Ahmed Abdalazeez ◽  
Denys Dutykh
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Numerical Study ◽  
Breaking Waves ◽  
Shallow Water Theory ◽  
Wave Runup ◽  
Coastal Slope ◽  
Long Wave ◽  
Nonlinear Shallow Water Theory ◽  
Runup Height

<p>The goal of this study is to investigate the effect of the bottom shape on wave runup. The obtained results have been confronted with available analytical predictions and a dedicated numerical simulation campaign has been carried out by the team. We study long wave runup on composite coastal profiles. Two types of beach profiles are considered. The Coastal Slope 1 consists of two merged plane beaches with lengths 1.2 m and 5 m and beach slopes tan α = 1:10 and tan β = 1:15 respectively. The Coastal Slope 2 also consists of two sections: plane beach with length 1.2 m and a beach slope α, which is merged with a convex (non-reflecting) beach. The latter is constructed in the way, that its total height and length remain the same as for the Coastal Slope 1.</p><p>The study is conducted with numerical (in silico) and experimental approaches.</p><p>Experiments have been conducted in the hydrodynamic flume of the Nizhny Novgorod State Technical University n.a. R.E. Alekseev. Both composite beach profiles were constructed in 2019. The Coastal Slope 1 consists of three parts made of aluminum. The plain beach part of the Coastal Slope 2 is also made of aluminum, and the convex profile consists of two parts made of curved PLEXIGLAS organic glass. The water surface oscillations are measured using capacitive and resistive wave gauges with recording frequencies of up to 80 Hz and 100 Hz respectively. Wave runup is measured by a capacitive string sensor installed along the slope.</p><p>A series of experiments on the generation and runup of regular wave trains with a period of 1s, 2s, 3s and 4s were carried out. The water level was kept constant for all experiments and was equal to 0.3 meters. Up to now, 21 experiments have been carried out (10 and 11 experiments for each Coastal Slope respectively).</p><p>A comparative numerical study is carried out in the framework of the nonlinear shallow water theory and the dispersive theory in the Boussinesq approximation.</p><p>As a result, we compare the long wave dynamics on these two bottom profiles and discuss the influence of nonlinearity and dispersion on the characteristics of wave runup. It is shown numerically that, in the framework of the nonlinear shallow water theory, the runup height on the Coastal Slope 2 tends to exceed the corresponding runup height on the Coastal Slope 1, that also agrees with our previous results (Didenkulova et al. 2009; Didenkulova et al. 2018). Taking dispersion into account leads to an increase in the spread in values of the wave runup height. As a consequence, individual cases when the runup height on the Coastal Slope 1 is higher than on the Coastal Slope 2 have been observed. In experimental data, such cases occur more often, so that the advantage of one slope over another is no longer obvious. Note also that the most nonlinear breaking waves with a period of 1s have a greater runup height on Coastal Slope 2 for both models and most experimental data.</p>

Modelling of Moisture Movement in Wood during Outdoor Storage

2001 ◽  
Vol 6 (2) ◽  
pp. 3-14 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
I. Juodeikienė ◽  
A. Kajalavičius
Keyword(s):  
Experimental Data ◽  
Finite Difference ◽  
Climatic Conditions ◽  
Two Dimensional ◽  
Moisture Movement ◽  
Finite Difference Technique ◽  
Long Term Storage ◽  
Space Formulation ◽  
Term Storage

A model of moisture movement in wood is presented in this paper in a two-dimensional-in-space formulation. The finite-difference technique has been used in order to obtain the solution of the problem. The model was applied to predict the moisture content in sawn boards from pine during long term storage under outdoor climatic conditions. The satisfactory agreement between the numerical solution and experimental data was obtained.

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

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