Implicit time discretization schemes for least‐squares finite element formulations to model incompressible flows

Abstract

In the present contribution different implicit time integration schemes to model incompressible flow problems are investigated. Amongst the tested methods are the fully implicit Newmark, Houbolt and Crank-Nicolson schemes.The first-order system for the proposed formulation is given in terms of stresses and velocities as introduced in [1]. Raviart-Thomas and standard Lagrange interpolation functions are used to approximate the stresses and velocities, respectively.For the comparison of all time discretization schemes, the unsteady two-dimensional laminar flow around a cylinder at Reynolds number Re = 100 is chosen. For a rating on the accuracy, the obtained results for the drag coefficient are benchmarked against reference solutions by [2].

A least‐squares finite element approach to model fluid‐structure interaction problems

“…with the pressure p, the fluid density ρ f and the kinematic viscosity ν f . For more details, see, e.g., [1], [5] and [6]. To consider the deformation of the fluid domain, an Arbitrary-Lagrangian-Eulerian framework is used by introducing a mesh velocityṽ, which is determined with a linear elasticity approach and subtracted from the fluid velocity.…”