Numerical Analysis and Scientific Computing Preprint Seria An octree-based solver for the incompressible Navier-Stokes equations with enhanced stability and low dissipation

An octree-based solver for the incompressible Navier-Stokes equations with enhanced stability and low dissipation

The paper introduces a finite difference solver for the unsteady incompressible Navier-Stokes equations based on adaptive cartesian octree grids. The method extends a stable staggered grid finite difference scheme to the graded octree meshes. It is found that a straightforward extension is prone to produce spurious oscillatory velocity modes on the fine-to-coarse grids interfaces. A local linea...

Numerical Analysis and Scientific Computing Preprint Seria LU factorizations and ILU preconditioning for stabilized discretizations of incompressible Navier-Stokes equations

Numerical Analysis and Scientific Computing Preprint Seria Deconvolution-based nonlinear filtering for incompressible flows at moderately large Reynolds numbers

SUMMARY We consider a Leray model with a deconvolution-based indicator function for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of few thousand) with under-resolved meshes. For the implementation of the model, we adopt a three-step algorithm called evolve-filter-relax (EFR) that requires (i) the solution of a Navier-Stokes problem, (ii) the solu...

An Enhanced Flux Treatment in Solving Incompressible Flow in a Forward-Facing Step

The aim of this paper is to give a detailed effect of several parameters such as step height, Reynolds number, contraction ratio, and temperature difference between the entrance and solid boundaries, of a forward-facing step. An accurate length of separation and reattachment zones are achieved. A finite-volume method (FVM) has been developed to study incompressible flow in a forward-facing step...

Numerical Analysis and Scientific Computing Preprint Seria A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle

The paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasiLagrangian formulation of the problem and handles geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL tim...