High Order Numerical Methods to Three Dimensional Delta Function Integrals in Level Set Methods

2010 ◽  
Vol 32 (3) ◽  
pp. 1288-1309 ◽  
Author(s):  
Xin Wen
Keyword(s):  
Numerical Methods ◽  
Level Set ◽  
Level Set Methods ◽  
Three Dimensional ◽  
Delta Function ◽  
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.

High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method

2012 ◽  
Vol 12 (1) ◽  
pp. 1-41 ◽  
Author(s):  
Thibault Pringuey ◽  
R. Stewart Cant
Keyword(s):  
Level Set ◽  
Three Dimensional ◽  
Unstructured Meshes ◽  
High Order ◽  
Convex Polyhedra ◽  
Two Phase ◽  
High Order Schemes ◽  
Flow Problems ◽  
Mixed Element ◽  
Areas Of Interest

AbstractIn this article, we detail the methodology developed to construct arbitrarily high order schemes — linear and WENO — on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set.

scholarly journals Level set methods for detonation shock dynamics using high-order finite elements

2017 ◽  
Author(s):  
V. A. Dobrev ◽  
F. C. Grogan ◽  
T. V. Kolev ◽  
R Rieben ◽  
V. Z. Tomov
Keyword(s):  
Finite Elements ◽  
Level Set ◽  
Level Set Methods ◽  
High Order ◽  
Shock Dynamics ◽  
Detonation Shock

scholarly journals Enablers for high-order level set methods in fluid mechanics

2015 ◽  
Vol 79 (12) ◽  
pp. 654-675 ◽  
Author(s):  
Francky Luddens ◽  
Michel Bergmann ◽  
Lisl Weynans
Keyword(s):  
Fluid Mechanics ◽  
Level Set ◽  
Level Set Methods ◽  
High Order
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