On the unsteady Stokes problem with a nonlinear open artificial boundary condition modelling a singular load
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.
Domains
Mathematics [math] Analysis of PDEs [math.AP] Mathematics [math] Numerical Analysis [math.NA] Physics [physics] Mechanics [physics] Fluid mechanics [physics.class-ph] Physics [physics] Physics [physics] Fluid Dynamics [physics.flu-dyn] Engineering Sciences [physics] Mechanics [physics.med-ph] Fluids mechanics [physics.class-ph] Computer Science [cs] Modeling and Simulation
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