Several competing artificial compressibility methods for the incompressible flow equations are examined using high-order flux reconstruction method. The established method (ACM) of \citet{Chorin1967} is compared to alternative entropically damped (EDAC) \citet{Clausen2013}, as well an ACM formulation with hyperbolised diffusion. While former requires solution be converged a divergence free stat...

We present a new wavelet numerical scheme for the discretization of Navier-Stokes equations with physical boundary conditions. The temporal discretization of the method is inspired from the projection method. Helmholtz-Hodge decomposition using divergence-free and curl-free wavelet bases satisfying physical boundary conditions allows to define the projection operator. This avoids the use of Poi...

Many uid ow problems of practical interest|particularly at high Reynolds num-ber|are characterized by small regions of complex and rapidly-varying uid motion surrounded by larger regions of relatively smooth ow. EEcient solution of such problems requires an adaptive mesh reenement capability to concentrate computational eeort where it is most needed. We present in this paper a fractional-step v...

Article history: Received 15 January 2009 Received in revised form 16 April 2010 Accepted 28 May 2010 Available online 8 June 2010

We consider a defect correction method (DCM) which has been used extensively in applications where solutions have sharp transition regions, such as high Reynolds number fluid flow problems. A reliable a posteriori error estimator is derived for a defect correction method. The estimator is further studied for two examples: (a) the case of a linear-diffusion, nonlinear convection-reaction equatio...