A characteristic‐based method for incompressible flows

Abstract

A new characteristic-based method for the solution of the 2D laminar incompressible Navier-Stokes equations is presented. For coupling the continuity and momentum equations, the artificial compressibility formulation is employed. The primitives variables (pressure and velocity components) are defined as functions of their values on the characteristics. The primitives variables on the characteristics are calculated by an upwind differencing scheme based on the sign of the local eigenvalue of the Jacobian matrix of the convective fluxes. The upwind scheme uses interpolation formulae of third-order accuracy. The time discretization is obtained by the explicit Runge-Kutta method. Validation of the characteristic-based method is performed on two different cases: the flow in a simple cascade and the flow over a backwardfacing step.

Computing multi-mode shock-induced compressible turbulent mixing at late times

“…High-resolution methods were originally designed to address issues of accuracy, and physically-correct behaviour in the proximity of discontinuities such as shock waves, as well as contact discontinuities. ILES is the established numerical approach for compressible turbulent mixing but is also widely used in many other Bell and Colella (1989) and Drikakis et al (1994) have shown that non-oscillatory methods can also be used for incompressible flows. In this study, the incompressible and compressible Euler equations are solved by nonoscilatory methods (Drikakis and Rider 2004).…”

Implicit unfactored implementation of two-equation turbulence models in compressible Navier-Stokes methods

“…This method was first presented by Eberle [24] for the compressible Euler equations and was extended by Drikakis et al [25,26] to solve the incompressible Navier -Stokes equations. The inviscid equations are split into two one-dimensional equations.…”

“…In this paper, only the extensions of the method due to the incorporation of the convection terms of the turbulence transport equations are presented. For more details on the discretization of the inviscid fluxes of the incompressible and compressible Navier -Stokes equations, the reader is referred to References [24][25][26].…”

Embedded turbulence model in numerical methods for hyperbolic conservation laws

“…† The derivation ofŨ as function of U l in generalized curvilinear co-ordinates can be found in References [16] and [9] for 2D and 3D problems, respectively. Application of the above theorem in the case of the CB scheme ‡ shows that the CB scheme is ÿrst-, second- § and third-order accurate in both space and time when it is implemented in conjunction with the Euler, second-order TVD Runge-Kutta [24], and third-order TVD Runge-Kutta time-stepping schemes [24], respectively.…”