A high order term-by-term stabilization solver for incompressible flow problems

2012 ◽  
Vol 33 (3) ◽  
pp. 974-1007 ◽  
Author(s):  
T. C. Rebollo ◽  
M. G. Marmol ◽  
V. Girault ◽  
I. S. Munoz
Keyword(s):  
Incompressible Flow ◽  
Order Term ◽  
High Order ◽  
High Order Term ◽  
Flow Problems

scholarly journals Arithmetic expressions optimisation using dual polarity property

2003 ◽  
Vol 1 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Dragan Jankovic ◽  
Radomir Stankovic ◽  
Claudio Moraga
Keyword(s):  
Order Term ◽  
High Order ◽  
High Order Term ◽  
Experimental Results ◽  
Simple Relationship ◽  
Dual Polarity ◽  
The Given ◽  
Arithmetic Expressions

A method for optimisation of fixed polarity arithmetic expressions (FPAEs) based on dual polarity is proposed. The method exploits a simple relationship between two FPAEs for dual polarities. It starts from the zero polarity FPAE of the given function and calculates all FPAEs using the dual polarity route. Using one-bit check carries out conversion from one FPAE to another. Each term in an FPAE is processed by the proposed processing rule. Terms, which differ in a single position, can be substituted by a high order term (cube). Experimental results show efficiency of proposed method.

Analysis of the High Order Terms on Periodic Solution Bifurcations of the Generalized Duffing Systems

2013 ◽  
Vol 718-720 ◽  
pp. 1705-1710
Author(s):  
Shi Dong Chen ◽  
Zhi Qiang Wu
Keyword(s):  
Periodic Solution ◽  
Order Term ◽  
Singularity Theory ◽  
Multiple Scale ◽  
High Order ◽  
Duffing Equation ◽  
High Order Term ◽  
Bifurcation Equation ◽  
Bifurcation Diagrams

This paper focuses on the effectsof the high order term in Duffing equation. Firstly the averaging equation andthe bifurcation equation are deduced through the multiple scale method.Secondly, the transition sets and several different bifurcation diagrams areobtained based on the singularity theory. The result shows that the high order term induces richer bifurcationcharacteristics.

Theoretical Analysis and Engineering Implications for the High Order Term Solutions of the Mode II Type Creep Crack

2017 ◽  
Author(s):  
Yanwei Dai ◽  
Yinghua Liu ◽  
Yuh J. Chao
Keyword(s):  
Theoretical Analysis ◽  
Plane Strain ◽  
Order Term ◽  
Crack Tip ◽  
High Order ◽  
High Order Term ◽  
Mode I ◽  
Mode Ii ◽  
Mode I Crack ◽  
Creep Crack

The high order term (HOT) solutions of crack tip field should be taken into account in engineering applications due to their potential influences on the fracture toughness as well as the crack growth rate. Towards this end, the high order asymptotic analysis of mode II crack in a power-law creeping material under the plane strain condition is presented theoretically in this paper. By comparing among the three order term solution, HRR field and finite element calculations, it can be found that the proposed three order term solution is able to characterize the full field of mode II creep crack tip accurately. The high order term solution of mode II creep crack relies on the creep exponent, which is different from that of mode I crack case. There are two independent terms among these three terms of asymptotic solution for mode II creep crack, which indicates that there exists the constraint effect for the plane strain mode II creep crack though the effect of high order term may not be as significant as the mode I crack case. Based on the theoretical analysis, a modified time-dependent failure assessment diagram (TDFAD) for mode II creep crack is proposed by considering the high order term solution.

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.

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