On the unsteady Stokes problem with a nonlinear open artificial boundary condition modelling a singular load
type: Dataset
description: 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.
issued: 2026-05-11T05:28:44.107998
language: en
modified: 2026-05-11T05:28:44.108004
contact point: Organization
  fn: CCSD
keyword: 2010-msc-35a35-35j50-35j60-35j65-35k40-35k55-35k60-35q30-76d03-76d05-65m06-65m12-65n12
keyword: artificial-boundary
keyword: inflowoutflow-boundary-condition
keyword: infoeu-reposemanticspreprint
keyword: infoinfo-mocomputer-science-csmodeling-and-simulation
keyword: mathmath-apmathematics-mathanalysis-of-pdes-mathap
keyword: mathmath-namathematics-mathnumerical-analysis-mathna
keyword: non-stationary-stokes-problem
keyword: open-boundary-condition
keyword: physmecameflphysics-physicsmechanics-physicsfluid-mechanics-physicsclass-ph
keyword: physphysphys-flu-dynphysics-physicsphysics-physicsfluid-dynamics-physicsflu-dyn
keyword: preprints-working-papers-
keyword: singular-head-loss
keyword: spimecameflengineering-sciences-physicsmechanics-physicsmed-phfluids-mechanics-physicsc
keyword: unsteady-incompressible-viscous-flow
landing page: https://hal.science/hal-00820404

On the unsteady Stokes problem with a nonlinear open artificial boundary condition modelling a singular load
type: Distribution
format: HTML
issued: 2026-05-11T05:28:44.134594
modified: 2026-05-11T05:28:44.091974
access URL: https://hal.science/hal-00820404

test_moissonnage_selune
type: Agent