A high-order discontinuous Galerkin method for natural convection problems

Discontinuous Galerkin (DG) methods have proved to be very well suited for the construction of robust high-order numerical schemes on unstructured and possibly non conforming grids for a wide variety of problems. In this paper we consider natural convection flow problems and present a high-order DG method for their numerical solution. The...

Stabilized FEM for incompressible flow: A critical review and new trends

The numerical solution of the nonstationary, incompressible Navier-Stokes model can be split into linearized auxiliary problems of Oseen type. We present in a unique way different stabilization techniques of finite element schemes on isotropic and hybrid meshes. First we describe the state-of-the-art for the classical residual-based SUPG/PSPG...

An investigation of the performance of a high-order accurate Navier-Stokes code

A high-order accurate multi-block Navier-Stokes code is evaluated and tested by considering the flow over a cavity in two space dimensions. Both shear layer mode and wake mode are studied. The efficiency, robustness and flexibility of the code is demonstrated.

Bulk viscosity damping for accelerating convergence of compressible viscous flow solvers

In solution of the Euler equations in the steady state conditions, the error or residual waves are blamed for the reduction of convergence rate. These waves may be damped by adding a bulk viscosity term to the momentum equations. It was done to the Euler equations previously and in this work this method has been applied to the Navier-Stokes...

Energy stable finite element schemes and their applications to two-fluid flow problems

We present energy stable finite element schemes for two-fluid problems with interfacial tension. The interface is captured by solving numerically ordinary differential equations and the interface tension is brought in into the weak formulation of the finite element scheme. Some numerical results of rising bubble problems show the robustness and...

Computations of flows with interfaces using arbitrary Lagrangian Eulerian method

This work is devoted to the accurate simulation of incompressible two phase flows. The core of our methodology is the use of interface resolving meshes and the arbitrary Lagrangian-Eulerian (ALE) description of the fluid kinematics. Our numerical scheme is based on second order finite elements, a fractional step ? time discretisation, and a...

Real-time reduced basis techniques for Navier-Stokes equations: Optimization of parametrized bypass configurations

The reduced basis method on parametrized domains is applied to approximate blood flow through an arterial bypass. The aim is to provide (a) a sensitivity analysis for relevant geometrical quantities of interest in bypass configurations and (b) rapid and reliable prediction of integral functional outputs ( such as fluid mechanics indexes). The...