Finite difference solution of the 3-D Euler equations using a multistage Runge-Kutta method

2006 ◽  
pp. 108-112
Author(s):  
J. M. Barton ◽  
S. K. Yoon
Keyword(s):  
Finite Difference ◽  
Euler Equations ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Finite Difference Solution ◽  
Runge Kutta ◽  
Difference Solution

scholarly journals Analysis and optimization of nonlinear carrying performance of hydrostatic ram based on finite difference method and Runge–Kutta method

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985612 ◽  
Author(s):  
Yumo Wang ◽  
Zhifeng Liu ◽  
Qiang Cheng ◽  
Yongsheng Zhao ◽  
Yida Wang ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Dynamic Equilibrium ◽  
Dynamic Performance ◽  
Machining Accuracy ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Tip Position

Analyzing of nonlinear carrying performance of hydrostatic ram is among key research questions to improve heavy machine tools because the machining precision will be directly influenced by it. A dynamic model of nonlinear supporting characters for hydrostatic ram is developed in this work. Modified Reynolds equation is resolved by finite difference method numerically to determine the carrying capability. Dynamic equilibrium equation of hydrostatic ram under cutting force impact is solved by Runge–Kutta method to obtain the variation of tool tip position and evaluate the machining accuracy. An optimal oil supply rate allocation and oil pad size is proposed to improve the static and dynamic performance simultaneously based on method of bisection.

NEW METHOD FOR CHARACTERISTIC EVOLUTIONS IN NUMERICAL RELATIVITY

2013 ◽  
Vol 22 (08) ◽  
pp. 1350042 ◽  
Author(s):  
ZHOUJIAN CAO
Keyword(s):  
Cauchy Problem ◽  
Finite Difference ◽  
Differential Equations ◽  
Numerical Relativity ◽  
Einstein Equations ◽  
New Method ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Special Difference

The main task of numerical relativity is to solve Einstein equations with the aid of supercomputer. There are two main schemes to write Einstein equations explicitly as differential equations. One is based on 3 + 1 decomposition and reduces the Einstein equations to a Cauchy problem. The another takes the advantage of the characteristic property of Einstein equations and reduces them to a set of ordinary differential equations. The latter scheme is called characteristic formalism which is free of constraint equations in contrast to the corresponding Cauchy problem. Till now there is only one well developed code (PITT code) for characteristic formalism. In PITT code, special finite difference algorithm is adopted for the numerical calculation. And it is this special difference algorithm that restricts the numerical accuracy order to second-order. In addition, this special difference algorithm makes the popular Runge–Kutta method used in Cauchy problem not available. In this paper, we modify the equations for characteristic formalism. Based on our new set of equations, we can use usual finite difference method as done in usual Cauchy evolution. And Runge–Kutta method can also be adopted naturally. We develop a set of code in the framework of AMSS-NCKU code based on our new method and some numerical tests are done.

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