An Eulerian-Lagrangian approach to the Navier-Stokes equations

0 An Eulerian - Lagrangian Approach to the Navier - Stokes equations

Lagrangian Approximations and Weak Solutions of the Navier-Stokes Equations

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian re...

Arbitrary Lagrangian Eulerian Analysis of a Bidirectional Micro-Pump Using Spectral Elements

Performance analysis of a reversible micro-pump system is obtained by numerical simulations. The unsteady incompressible Navier–Stokes equations are solved in a moving micro-pump system using a spectral h/p element algorithm, employing an arbitrary Lagrangian Eulerian (ALE) formulation on structured/unstructured meshes. The performance of the micro-pump is evaluated as a function of the Reynold...

Implicit Surface Tension Formulation with a Lagrangian Surface mesh on an Eulerian Simulation Grid

We present a method for applying implicit forces on a Lagrangian mesh to an Eulerian discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has implicit and fully coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of surface tension force, which...

Output-based mesh adaptation for high order Navier-Stokes simulations on deformable domains

We present an output-based mesh adaptation strategy for Navier-Stokes simulations on deforming domains. The equations are solved with an arbitrary Lagrangian-Eulerian (ALE) approach, using a discontinuous Galerkin finiteelement discretization in both space and time. Discrete unsteady adjoint solutions, derived for both the state and the geometric conservation law, provide output error estimates...