Superconvergent second order Cartesian method for solving free boundary problem for invadopodia formation
GALLINATO, Olivier
Université de Bordeaux [UB]
Institut de Mathématiques de Bordeaux [IMB]
Modélisation Mathématique pour l'Oncologie [MONC]
Université de Bordeaux [UB]
Institut de Mathématiques de Bordeaux [IMB]
Modélisation Mathématique pour l'Oncologie [MONC]
POIGNARD, Clair
Modélisation Mathématique pour l'Oncologie [MONC]
Institut de Mathématiques de Bordeaux [IMB]
Modélisation Mathématique pour l'Oncologie [MONC]
Institut de Mathématiques de Bordeaux [IMB]
GALLINATO, Olivier
Université de Bordeaux [UB]
Institut de Mathématiques de Bordeaux [IMB]
Modélisation Mathématique pour l'Oncologie [MONC]
Université de Bordeaux [UB]
Institut de Mathématiques de Bordeaux [IMB]
Modélisation Mathématique pour l'Oncologie [MONC]
POIGNARD, Clair
Modélisation Mathématique pour l'Oncologie [MONC]
Institut de Mathématiques de Bordeaux [IMB]
< Leer menos
Modélisation Mathématique pour l'Oncologie [MONC]
Institut de Mathématiques de Bordeaux [IMB]
Idioma
en
Article de revue
Este ítem está publicado en
Journal of Computational Physics. 2017-06-15, vol. 339, p. 412 - 431
Elsevier
Resumen en inglés
In this paper, we present a superconvergent second order Cartesian method to solve a free boundary problem with two harmonic phases coupled through the moving interface. The model recently proposed by the authors and ...Leer más >
In this paper, we present a superconvergent second order Cartesian method to solve a free boundary problem with two harmonic phases coupled through the moving interface. The model recently proposed by the authors and colleagues describes the formation of cell protrusions. The moving interface is described by a level set function and is advected at the velocity given by the gradient of the inner phase. The finite differences method proposed in this paper consists of a new stabilized ghost fluid method and second order discretizations for the Laplace operator with the boundary conditions (Dirichlet, Neumann or Robin conditions). Interestingly, the method to solve the harmonic subproblems is superconvergent on two levels, in the sense that the first and second order derivatives of the numerical solutions are obtained with the second order of accuracy, similarly to the solution itself. We exhibit numerical criteria on the data accuracy to get such properties and numerical simulations corroborate these criteria. In addition to these properties, we propose an appropriate extension of the velocity of the level-set to avoid any loss of consistency, and to obtain the second order of accuracy of the complete free boundary problem. Interestingly, we highlight the transmission of the superconvergent properties for the static subproblems and their preservation by the dynamical scheme. Our method is also well suited for quasistatic Hele-Shaw-like or Muskat-like problems.< Leer menos
Palabras clave en inglés
Interface conditions
Superconvergence
Finite differences on Cartesian grids
boundary problem
2000 MSC: 65M06
Free
65M12
92C37
Orígen
Importado de HalCentros de investigación