The Multidimensional Optimal Order Detection method in the three-dimensional case: very high-order finite volume method for hyperbolic systems

2013 ◽  
Vol 73 (4) ◽  
pp. 362-392 ◽  
Author(s):  
S. Diot ◽  
R. Loubère ◽  
S. Clain
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Detection Method ◽  
Hyperbolic Systems ◽  
Three Dimensional ◽  
High Order ◽  
Dimensional Case ◽  
Optimal Order ◽  
Volume Method ◽  
Very High

scholarly journals A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation

2015 ◽  
Vol 25 (3) ◽  
pp. 529-537 ◽  
Author(s):  
Ricardo Costa ◽  
Gaspar J. Machado ◽  
Stéphane Clain
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Intramedullary Nail ◽  
High Order ◽  
Sixth Order ◽  
Finite Volume Scheme ◽  
Biharmonic Operator ◽  
Mean Values ◽  
Volume Method ◽  
Very High

Abstract A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.

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