On the unsteady Stokes problem with a nonlinear open artificial boundary condition modelling a singular load - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

## On the unsteady Stokes problem with a nonlinear open artificial boundary condition modelling a singular load

Philippe Angot

Connectez-vous pour contacter l'auteur

#### Abstract

We propose a practical nonlinear open boundary condition of Robin type for unsteady incompressible viscous flows taking account of the local inflow/outflow volume rate at an open artificial boundary with a singular load. The inflow/outflow parameters introduced in the modelling can be connected to the coefficient of singular head loss through Bernouilli's theorem of energy balance in a curl-free viscous flow. Then, we prove that this boundary condition leads to a well-posed unsteady nonlinear Stokes problem, i.e. global in time existence of a weak solution in dimension $d\leq 3$ with no restriction on the data. The proof is carried out by passing to the limit on a sequence of consistent discrete solutions of a non linear numerical scheme which approximates the original problem. The main ingredients are Schauder's fixed-point theorem and Aubin-Lions compactness argument.

### Dates and versions

hal-00820404 , version 1 (04-05-2013)

### Identifiers

• HAL Id : hal-00820404 , version 1

### Cite

Philippe Angot. On the unsteady Stokes problem with a nonlinear open artificial boundary condition modelling a singular load. 2013. ⟨hal-00820404⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

215 View