The Calculation of Ship Wave in Shallow Water by Finite Difference Method

2013 ◽  
Vol 409-410 ◽  
pp. 1461-1464
Author(s):  
Deng Hui ◽  
Zhi Hong Zhang ◽  
Jian Nong Gu
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Shallow Water ◽  
Difference Method ◽  
Integral Transform ◽  
Fourier Integral ◽  
Transform Method ◽  
The Mathematical Model ◽  
Supercritical Speed

Based on the shallow water wave potential flow theory and slender ship assumption, the mathematical model is established for calculating wave caused by ship moving at supercritical speed. The wave pattern caused by ship moving at supercritical speed in shallow water was calculated by using the finite difference method. The effects of channel wall were analyzed. The computed results were compared with the ones calculated by Fourier integral transform method and experiment. A good agreement exists between the calculated with experimental results. The mathematical model and the calculation method were validated.

Studi Perpindahan Panas Material pada Sistem Koordinat Segitiga

2017 ◽  
Vol 1 ◽  
pp. 114
Author(s):  
Imam Basuki ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
The Finite Difference Method ◽  
The Mathematical Model

<p class="Normal1"><strong><em>Abstract: </em></strong><em>Partial Differential Equations (PDP) Laplace equation can be applied to the heat conduction. Heat conduction is a process that if two materials or two-part temperature material is contacted with another it will pass heat transfer. Conduction of heat in a triangle shaped object has a mathematical model in Cartesian coordinates. However, to facilitate the calculation, the mathematical model of heat conduction is transformed into the coordinates of the triangle. PDP numerical solution of Laplace solved using the finite difference method. Simulations performed on a triangle with some angle values α and β</em></p><p class="Normal1"><strong><em> </em></strong></p><p class="Normal1"><strong><em>Keywords:</em></strong><em>  heat transfer, triangle coordinates system.</em></p><p class="Normal1"><em> </em></p><p class="Normal1"><strong>Abstrak</strong> Persamaan Diferensial Parsial (PDP) Laplace  dapat diaplikasikan pada persamaan konduksi panas. Konduksi panas adalah suatu proses yang jika dua materi atau dua bagian materi temperaturnya disentuhkan dengan yang lainnya maka akan terjadilah perpindahan panas. Konduksi panas pada benda berbentuk segitiga mempunyai model matematika dalam koordinat cartesius. Namun untuk memudahkan perhitungan, model matematika konduksi panas tersebut ditransformasikan ke dalam koordinat segitiga. Penyelesaian numerik dari PDP Laplace diselesaikan menggunakan metode beda hingga. Simulasi dilakukan pada segitiga dengan beberapa nilai sudut  dan  </p><p class="Normal1"><strong> </strong></p><p class="Normal1"><strong>Kata kunci :</strong> perpindahan panas, sistem koordinat segitiga.</p>

Simulation of Hydraulic Pipeline Pressure Transients Accompanying Cavitation and Gas Bubbles Using Matlab/Simulink

2006 ◽  
Author(s):  
Jiang Dan ◽  
Songjing Li
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Gas Bubbles ◽  
Simulation Method ◽  
Low Pressure ◽  
Matlab Simulink ◽  
Pressure Transients ◽  
The Mathematical Model

In order to predict pressure transients accompanying cavitation and gas bubbles in hydraulic pipeline operating at low pressure, a mathematical model and a simulation method are studied. The mathematical model is based on the two basic equations of motion and continuity. The growing and collapsing of cavitation and gas bubbles accompanying pressure pulsations are modelled to calculate the volumes of cavitation and gas bubbles. The pipeline dynamic friction model is introduced. Meanwhile, a simulation method, using finite difference method and Matlab/Simulink platform, is developed to handle the prediction of pressure transients. Finally an example of fluid transients inside hydraulic pipeline is simulated after a downstream valve is closed rapidly. Simulation results show that, for a certain example pipeline, the mathematical model can handle the prediction of pressure transients accompanying cavitation and gas bubbles in low pressure pipeline. The use of combining finite difference method with Matlab/Simulink platform provides a relatively simple and effective tool to understand the nature of pressure transients accompanying cavitation and gas bubbles.

A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE’s

2014 ◽  
Vol 6 (5) ◽  
pp. 693-698 ◽  
Author(s):  
Kosuke Abe ◽  
Nobuyuki Higashimori ◽  
Masayoshi Kubo ◽  
Hiroshi Fujiwara ◽  
Yuusuke Iso
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Hyperbolic Partial Differential Equations ◽  
View Point ◽  
Rounding Errors ◽  
The Finite Difference Method

AbstractThe Courant-Friedrichs-Lewy condition (The CFL condition) is appeared in the analysis of the finite difference method applied to linear hyperbolic partial differential equations. We give a remark on the CFL condition from a view point of stability, and we give some numerical experiments which show instability of numerical solutions even under the CFL condition. We give a mathematical model for rounding errors in order to explain the instability.

Modeling of pneumatic dual reciprocating bellows pump with flexible linkage

2020 ◽  
pp. 095440622093672
Author(s):  
Hu Liang ◽  
Gao Zhi-jian ◽  
Ge Tian-yi ◽  
Ruan Xiao-dong ◽  
Fu Xin
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Control Parameters ◽  
Effective Solution ◽  
Mechanical Parts ◽  
And Control ◽  
Flexible Linkage

Pneumatic dual reciprocating bellows pump has been widely used in chemical transportation due to its good sealing and anticorrosion performances. Nevertheless, the large outlet pulsation limits its performances on precise transportation and control of the fluid. Although the design of employing flexible linkage between the bellows has been proposed as an effective solution for this shortcoming, the design, manufacture, and control of the pump also become much more complicated. This paper presents a mathematical model to formulate the effects of structural, geometric, and control parameters to the output pulsation of pneumatic dual reciprocating bellows pump with flexible linkage. It is a dynamic model unifying several sub-models expressing the pneumatic, hydraulic, and mechanical parts in the pump, respectively. To ensure the accuracy, some special experiments are also employed to identify some key parameters in the model that cannot be determined directly. In addition, finite difference method is employed to solve the nonlinear equations. The model is well verified by comparing its computation results with experimental data. We believe that this study is valuable for guiding the design of pneumatic dual reciprocating bellows pump and optimizing its output pulsation.

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