Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Conservative high-order finite-difference schemes for low-Mach number flows

High order conservative finite difference scheme for variable density low Mach number turbulent flows

The high order conservative finite difference scheme of Morinishi et al. [Y. Morinishi, O.V. Vasilyev, T. Ogi, Fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations, J. Comput. Phys. 197 (2004) 686] is extended to simulate variable density flows in complex geometries with cylindrical or cartesian non-uniform meshes. The formulation discretely...

High-order finite difference schemes for incompressible flows

This paper presents a new high order approach to the numerical solution of the incompressible Stokes and Navier-Stokes equations. The class of schemes developed is based upon a velocity-pressure-pressure gradient formulation which allows: (i) high order finite difference stencils to be applied on nonstaggered grids; (ii) high order pressure gradient approximations to be made using standard Padé...

High Order Compact Finite Difference Schemes for Solving Bratu-Type Equations

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...

Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow

Conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations. Existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out. In particular, it is found that ...