A quasi-elliptic transformation for moving boundary problems with large anisotropic deformations

On the elliptic mesh generation in domains containing multiple inclusions and undergoing large deformations

“…On the other hand, the coordinate lines normal to the interface must intersect them nearly orthogonally. Keeping these in mind, Dimakopoulos and Tsamopoulos [13], concluded that the following system of quasi-elliptic partial differential equations combines these features…”

Simulation of incompressible viscous flows around moving objects by a variant of immersed boundary‐lattice Boltzmann method

“…So, the physical boundary condition can be implemented directly. One of popular methods in this category is the use of time-dependent coordinate transformation [1][2][3][4], in which the moving physical domain is transformed into a fixed computational domain, and all the numerical computations are easily performed in the computational domain. This approach is very efficient for the case where the whole object moves at the same mode.…”

A direct comparison between volume and surface tracking methods with a boundary-fitted coordinate transformation and third-order upwinding

“…(8) is the transformed equation of continuity for incompressible fluids, Eqs. (9) and (10) are the transformed radial and axial components of the momentum equation, while Eq. (11) give the transformed stress components for Newtonian fluids.…”

“…We approximate the Dirac function appearing in Eqs. (9) and (10) using the gradient of the volume function. This function is indeed an approximation to the Dirac function, since it is zero everywhere in the computational domain except for thin transition regions of distance comparable to the mesh spacing O(Dx, Dy) where the interface exists.…”

“…Most finite element as well as spectral methods are developed around a Lagrangian approach and have been used successfully in calculating time dependent solutions of both single [4] and twophase flows [5][6][7][8] in which free surfaces are involved. More recently, we advanced a mesh generation method based on solving a set of elliptic differential equations that can follow very large interface distortions, but still additional programming effort is needed to allow for interface breaking and merging [9,10]. Because we are further interested in readily predicting the above mentioned flow regimes and how they evolve, using either FEM or spectral methods in combination with a Lagrangian approach is precluded, since they cannot, at the present time, model such complex breaking and reforming interfaces [11].…”