Abstract. This work is concerned with the simulation of compressible flow in time dependent domains. We present an ALE (Arbitrary Lagrangian-Eulerian) formulation of the Navier-Stokes equations describing compressible flow, discretize them in space by the discontinous Galerkin method and introduce a semi-implicit linearized time stepping for the numerical solution of the complete problem. We pr...

A penalization method is applied to model the interaction of large Mach number compressible flows with obstacles. A supplementary term is added to the compressible Navier-Stokes system, seeking to simulate the effect of the Brinkmanpenalization technique used in incompressible flow simulations including obstacles. We present a computational study comparing numerical results obtained with this m...

This is a survey of some recent results on the existence of globally defined weak solutions to the Navier-Stokes equations of a viscous compressible fluid with a general barotropic pressure-density relation.

In this paper, we prove the local well-posedness in critical Besov spaces for the compressible Navier-Stokes equations with density dependent viscosities under the assumption that the initial density is bounded away from zero.

In this paper we focus on an existence of a weak solution to a system describing a self-propelled motion of a single deformable body in a viscous compressible fluid which occupies a bounded domain in the 3 dimensional Euclidean space. The considered governing system for the fluid is the isentropic compressible Navier-Stokes equation. We prove an existence of a weak solution up to a collision.

Abstract: We study a nonlocal modification of the compressible Navier-Stokes equations in mono dimensional case with a boundary condition characteristic for the free boundaries problem. From the formal point of view our system is an intermediate between the Euler and Navier-Stokes equations. Under certain assumptions, imposed on initial data and viscosity coefficient, we obtain the local and gl...

Microfluidics is a multidisciplinary area founding applications in several fields such as the aerospace industry. Microelectromechanical systems (MEMS) are mainly adopted for flow control, micropower generation and for life support and environmental control for space applications. Microflows are modeled relying on both a continuum and molecular approach. In this paper, the compressible Navier–S...

In this lecture, we will particularly analyze the effect of the shallowness on the Navier Stokes equations, together with anisotropic eddy viscosities. We will derive as an asymptotic model the hydrostatic approximation of the Navier Stokes equations. We will present a stable mixed 3D-FEM discretization, which allows for the computation of the 3D-velocity as a whole. Let us emphasize that verti...

Both the particle based Direct Simulation Monte Carlo (DSMC) method and a compressible Navier-Stokes based continuum method are used to investigate the flow inside micronozzles and to predict the performance of such devices. For the Navier-Stokes approach, both slip and no-slip boundary conditions are applied. Moreover, the two methods have been coupled to be used together in a hybrid particle-...

This paper presents a novel semi-implicit hybrid finite volume / element (FV/FE) scheme for the numerical solution of incompressible and weakly compressible Navier-Stokes equations on moving unstructured meshes using direct Arbitrary-Lagrangian-Eulerian (ALE) formulation. The is based suitable splitting governing partial differential into subsystems employs staggered grid arrangement, where pre...