Energy-decreasing continuum flows of geometric order parameters are considered. The dynamics of pattern formation for an arbitrary geometric quantity is derived using a generalization of Darcy’s law based on the geometric nature of the order parameter. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanic...

We consider a monolithic scheme for fluid–structure interaction problems involving an incompressible quasi-Newtonian fluid. The monolithic formulation is obtained using the Arbitrary Lagrangian Eulerian (ALE) method with matching conditions at the fluid–structure interface. The stability and error analysis are performed for the finite element approximation. Finally, some numerical experiments t...

Laser plasma is modeled by Lagrangian hydrodynamical equations including heat conductivity and laser absorption. The hyperbolic part of the model is treated by Arbitrary Lagrangian Eulerian (ALE) method which avoids moving mesh distortion and parabolic heat conductivity part is treated by splitting and mimetic method. High velocity laser accelerated disc impact problems for which standard Lagra...

Because of different behavior of reservoir water and dam material, the determination of hydrodynamic pressure during earthquake is very complicated. Thus, different formulations have been presented for modeling of the dam reservoir system under dynamic loading such as earthquake. These formulations can be categorized into two general groups, which are Lagrangian and Eulerian, each having advant...

Galilean invariance is one of the key requirements of many physical models adopted in theoretical and computational mechanics. Spurred by recent research developments in shock hydrodynamics computations [13], a detailed analysis on the principle of Galilean invariance in the context of SUPG operators is presented. It was observed in [13] that lack of Galilean invariance can yield catastrophic i...