Error analysis of fully discrete velocity-correction methods for incompressible flows

Vector and scalar penalty-projection methods - for incompressible and variable density flows

This work deals with the solution of Navier-Stokes equations governing incompressible flows with variable density, e.g. [10], or dilatable flows for which the Boussinesq approximation is no more valid like low Mach number flows, e.g. [5]. In these cases, the divergence constraint makes the fully-coupled system to solve at each time step for the velocity and dynamic pressure very ill-conditioned...

A Divergence-free Velocity Reconstruction for Incompressible Flows

In incompressible flows with vanishing normal velocities at the boundary, irrotational forces in the momentum equations should be balanced completely by the pressure gradient. Unfortunately, nearly all available discretization methods for incompressible flows violate this property. The origin of the problem is that discrete velocity approximations of incompressible flows are usually not diverge...

H(div) conforming and DG methods for incompressible Euler’s equations

H(div) conforming and discontinuous Galerkin (DG) methods are designed for incompressible Euler’s equation in two and three dimension. Error estimates are proved for both the semi-discrete method and fully-discrete method using backward Euler time stepping. Numerical examples exhibiting the performance of the methods are given.

Velocity-Correction Projection Methods For Incompressible Flows

A robust, colocated, implicit algorithm for direct numerical simulation of compressible, turbulent flows

A non-dissipative, robust, implicit algorithm is proposed for direct numerical and large-eddy simulation of compressible turbulent flows. The algorithm addresses the problems caused by low Mach numbers and under-resolved high Reynolds numbers. It colocates variables in space to allow easy extension to unstructured grids, and discretely conserves mass, momentum and total energy. The Navier–Stoke...