Higher-order compact scheme for high-performance computing of stratified rotating flows

A transient higher order compact scheme for incompressible viscous flows on geometries beyond rectangular

In this paper, we propose an implicit high-order compact (HOC) finite-difference scheme for solving the two-dimensional (2D) unsteady Navier–Stokes (N–S) equations on irregular geometries on orthogonal grids. Our scheme is second order accurate in time and fourth order accurate in space. It is used to solve three pertinent fluid flow problems, namely, the flow decayed by viscosity, the lid-driv...

High Order Modified Weighted Compact Scheme for High Speed Flow

The critical problem of CFD is perhaps an accurate approximation of derivatives for a given discrete data set. Based on our previous work on the weighted compact scheme (WCS), a modified weighted compact scheme (MWCS) has been developed. Similar to WENO, three high order candidates, left, right, and central, are constructed by Hermite polynomials. According to the smoothness, three weights are ...

Unbalanced instabilities of rapidly rotating stratified shear flows

The linear stability of a rotating, stratified, inviscid horizontal plane Couette flow in a channel is studied in the limit of strong rotation and stratification. Two dimensionless parameters characterize the flow: the Rossby number ǫ, defined as the ratio of the shear to the Coriolis frequency and assumed small, and the ratio s of the Coriolis frequency to the buoyancy frequency, assumed to sa...

Second-order scheme for quadrature-based velocity high order moment methods for disperse two-phase flows

A Compact Fourth-Order Finite Difference Scheme for Unsteady Viscous Incompressible Flows

In this paper, we extend a previous work on a compact scheme for the steady Navier Stokes equations [Li, Tang, and Fornberg (1995), Int. J. Numer. Methods Fluids, 20, 1137 1151] to the unsteady case. By exploiting the coupling relation between the streamfunction and vorticity equations, the Navier Stokes equations are discretized in space within a 3_3 stencil such that a fourth order accuracy i...