An efficient second-order accurate cut-cell method for solving the variable coefficient Poisson equation with jump conditions on irregular domains

2006 ◽  
Vol 52 (7) ◽  
pp. 723-748 ◽  
Author(s):  
Hua Ji ◽  
Fue-Sang Lien ◽  
Eugene Yee
Keyword(s):  
Poisson Equation ◽  
Variable Coefficient ◽  
Second Order ◽  
Jump Conditions ◽  
Irregular Domains ◽  
Cell Method ◽  
Cut Cell

A Second-Order-Accurate Symmetric Discretization of the Poisson Equation on Irregular Domains

2002 ◽  
Vol 176 (1) ◽  
pp. 205-227 ◽  
Author(s):  
Frederic Gibou ◽  
Ronald P. Fedkiw ◽  
Li-Tien Cheng ◽  
Myungjoo Kang
Keyword(s):  
Poisson Equation ◽  
Second Order ◽  
Irregular Domains ◽  
The Poisson Equation

scholarly journals Numerical Method for Solving Matrix Coefficient Elliptic Equation on Irregular Domains with Sharp-Edged Boundaries

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Liqun Wang ◽  
Liwei Shi
Keyword(s):  
Finite Element ◽  
Elliptic Equation ◽  
Numerical Method ◽  
Piecewise Linear ◽  
Second Order ◽  
Three Dimensions ◽  
Matrix Coefficient ◽  
Jump Conditions ◽  
Irregular Domains ◽  
Nonsmooth Boundary

We present a new second-order accurate numerical method for solving matrix coefficient elliptic equation on irregular domains with sharp-edged boundaries. Nontraditional finite element method with non-body-fitting grids is implemented on a fictitious domain in which the irregular domains are embedded. First we set the function and coefficient in the fictitious part, and the nonsmooth boundary is then treated as an interface. The emphasis is on the construction of jump conditions on the interface; a special position for the ghost point is chosen so that the method is more accurate. The test function basis is chosen to be the standard finite element basis independent of the interface, and the solution basis is chosen to be piecewise linear satisfying the jump conditions across the interface. This is an efficient method for dealing with elliptic equations in irregular domains with non-smooth boundaries, and it is able to treat the general case of matrix coefficient. The complexity and computational expense in mesh generation is highly decreased, especially for moving boundaries, while robustness, efficiency, and accuracy are promised. Extensive numerical experiments indicate that this method is second-order accurate in the L∞ norm in both two and three dimensions and numerically very stable.

scholarly journals A second-order cut-cell method for the numerical simulation of 2D flows past obstacles

2012 ◽  
Vol 65 ◽  
pp. 80-91 ◽  
Author(s):  
François Bouchon ◽  
Thierry Dubois ◽  
Nicolas James
Keyword(s):  
Numerical Simulation ◽  
Second Order ◽  
Cell Method ◽  
Cut Cell

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
Author(s):  
B. Bandyrskii ◽  
I. Lazurchak ◽  
V. Makarov ◽  
M. Sapagovas
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Integral Condition ◽  
Second Order ◽  
Computational Results ◽  
Discrete Method ◽  
Complex Eigenvalues ◽  
Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

Cartesian cut-cell method for axisymmetric separating body flows

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 905-911
Author(s):  
G. Yang ◽  
D. M. Causon ◽  
D. M. Ingram
Keyword(s):  
Cell Method ◽  
Cut Cell ◽  
Cartesian Cut

Cut-cell method based large-eddy simulation of tip-leakage flow

2015 ◽  
Vol 27 (7) ◽  
pp. 075106 ◽  
Author(s):  
Alexej Pogorelov ◽  
Matthias Meinke ◽  
Wolfgang Schröder
Keyword(s):  
Large Eddy Simulation ◽  
Leakage Flow ◽  
Tip Leakage Flow ◽  
Tip Leakage ◽  
Cell Method ◽  
Eddy Simulation ◽  
Cut Cell ◽  
Large Eddy
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