Solving moving interface problems using a higher order accurate finite difference scheme

2017 ◽  
Author(s):  
H. V. R. Mittal ◽  
Rajendra K. Ray
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Higher Order ◽  
Interface Problems ◽  
Moving Interface ◽  
Moving Interface Problems

scholarly journals A Parallel Second Order Cartesian Method for Elliptic Interface Problems

2012 ◽  
Vol 12 (5) ◽  
pp. 1562-1587 ◽  
Author(s):  
Marco Cisternino ◽  
Lisl Weynans
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Numerical Study ◽  
Elliptic Problems ◽  
Two Dimensions ◽  
Transmission Conditions ◽  
Second Order ◽  
Interface Problems ◽  
Elliptic Interface Problems

AbstractWe present a parallel Cartesian method to solve elliptic problems with complex immersed interfaces. This method is based on a finite-difference scheme and is second-order accurate in the whole domain. The originality of the method lies in the use of additional unknowns located on the interface, allowing to express straightforwardly the interface transmission conditions. We describe the method and the details of its parallelization performed with the PETSc library. Then we present numerical validations in two dimensions, assorted with comparisons to other related methods, and a numerical study of the parallelized method.

scholarly journals Convergence of a higher order finite difference scheme for two-phase Stefan problems.

2021 ◽  
Vol 1936 (1) ◽  
pp. 012007
Author(s):  
R Martínez-Rosado ◽  
F Castillo-Aranguren ◽  
R D Santiago-Acosta ◽  
E M Hernández-Cooper ◽  
J A Otero-Hernández
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Higher Order ◽  
Two Phase ◽  
Stefan Problems
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