Conditions at the downstream boundary for simulations of viscous, incompressible flow
SIAM Journal on Scientific and Statistical Computing
Unstructured spectral element methods for simulation of turbulent flows
Journal of Computational Physics
Least-Squares Finite Element Method for the Stokes Problem with Zero Residual of Mass Conservation
SIAM Journal on Numerical Analysis
Analysis of Least-Squares Finite Element Methods for the Navier--Stokes Equations
SIAM Journal on Numerical Analysis
Issues Related to Least-Squares Finite Element Methods for the Stokes Equations
SIAM Journal on Scientific Computing
Least-squares spectral elements applied to the Stokes problem
Journal of Computational Physics
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
On mass conservation in least-squares methods
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Direct Minimization of the least-squares spectral element functional - Part I: Direct solver
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.48 |
In the weak form Galerkin formulation for incompressible flows, the pressure has a well-understood role. At all times, it may be interpreted as a Lagrange multiplier that enforces the divergence-free constraint on the velocity field. This is not the case in least-squares formulations for incompressible flows, where the divergence-free constraint is enforced in a least-squares sense in a variational setting of residual minimization. Thus, the role of the pressure in a least-squares formulation is rather vague. We find that this lack of velocity-pressure coupling in least-squares formulations may induce spurious temporal pressure oscillations when using the non-stationary form of the equations. We present a least-squares formulation with improved velocity-pressure coupling, based on the use of a regularized divergence-free constraint. A first-order system least-squares (FOSLS) approach based on velocity, pressure and vorticity is used to allow the use of practical C0 element expansions in the finite element model. We use high-order spectral element expansions in space and second- and third-order time stepping schemes. Excellent conservation of mass and accuracy of computed pressure metrics are demonstrated in the numerical results.