Investigating the Multi-layered Richtmyer-Meshkov Instability with High-Order Accurate Numerical Methods

2015 ◽  
pp. 1095-1100
Author(s):  
Marc T. Henry de Frahan ◽  
Pooya Movahed ◽  
Eric Johnsen
Keyword(s):  
Numerical Methods ◽  
High Order

Optimization of the Navy’s three-dimensional mine impact burial prediction simulation model, Impact35, using high-order numerical methods

2021 ◽  
pp. 154851292110286
Author(s):  
Athanasios Donas ◽  
Ioannis Famelis ◽  
Peter C Chu ◽  
George Galanis
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Prediction Model ◽  
Simulation Model ◽  
Three Dimensional ◽  
Simulation System ◽  
High Order ◽  
Alternative Methodology ◽  
Runge Kutta ◽  
Fifth Order

The aim of this paper is to present an application of high-order numerical analysis methods to a simulation system that models the movement of a cylindrical-shaped object (mine, projectile, etc.) in a marine environment and in general in fluids with important applications in Naval operations. More specifically, an alternative methodology is proposed for the dynamics of the Navy’s three-dimensional mine impact burial prediction model, Impact35/vortex, based on the Dormand–Prince Runge–Kutta fifth-order and the singly diagonally implicit Runge–Kutta fifth-order methods. The main aim is to improve the time efficiency of the system, while keeping the deviation levels of the final results, derived from the standard and the proposed methodology, low.

Numerical methods with a high order of accuracy applied in the quantum system

1996 ◽  
Vol 104 (6) ◽  
pp. 2275-2286 ◽  
Author(s):  
Wusheng Zhu ◽  
Xinsheng Zhao ◽  
Youqi Tang
Keyword(s):  
Numerical Methods ◽  
Quantum System ◽  
High Order ◽  
Order Of Accuracy ◽  
High Order Of Accuracy

scholarly journals High-Order Energy and Linear Momentum Conserving Methods for the Klein-Gordon Equation

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 200 ◽  
Author(s):  
He Yang
Keyword(s):  
Numerical Methods ◽  
Gordon Equation ◽  
Free Particle ◽  
High Order ◽  
Linear Momentum ◽  
Relativistic Quantum Mechanics ◽  
Optimal Error Estimates ◽  
Numerical Schemes ◽  
Klein Gordon ◽  
Klein Gordon Equation

The Klein-Gordon equation is a model for free particle wave function in relativistic quantum mechanics. Many numerical methods have been proposed to solve the Klein-Gordon equation. However, efficient high-order numerical methods that preserve energy and linear momentum of the equation have not been considered. In this paper, we propose high-order numerical methods to solve the Klein-Gordon equation, present the energy and linear momentum conservation properties of our numerical schemes, and show the optimal error estimates and superconvergence property. We also verify the performance of our numerical schemes by some numerical examples.

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