The simulation of inviscid, compressible flows using an upwind kinetic method on unstructured grids

Abstract

SUMMARYA kinetic flux-vector-splitting method has been used to solve the Euler equations for inviscid, compressible flow on unstructured grids. This method is derived from the Boltzmann equation and is an upwind, cellcentred, finite volume scheme with an explicit time-stepping procedure. The Delaunay triangulation has been used to generate the grids. The approach is demonstrated for three flow field simulations, namely the subsonic flow over a two-component high-lift aerofoil, the transonic flow over an aerofoil and the supersonic flow in a channel.

A new flux‐limiting approach–based kinetic scheme for the Euler equations of gas dynamics

“…where X ± and Y are given by (11). With the approximation (22) and the new moments (23) defined, the -moment of the Boltzmann level flux-limited scheme (17) becomes…”

“…The dissipation control parameter used in m‐KFVS has been devised using some physical arguments and the scheme performs well in subsonic, supersonic, and hypersonic flow regimes. The KFVS‐type schemes have also been formulated in meshless framework and on unstructured grids …”

“…The KFVS-type schemes have also been formulated in meshless framework 21 and on unstructured grids. 22,23 This paper uses the Sweby's flux-limited method 24 to discretize the collisionless Boltzmann equation and then moment is taken to get a Euler level scheme which is referred to as flux-limited kinetic solver (FLKS). The basic motivation behind using flux limiting at the Boltzmann level is to explore the possibility of achieving high resolution and close to second-order convergence at Euler level by moment method and hence assessing the correspondence between Boltzmann and Euler level in transferring the resolution and order of accuracy property from one level to another.…”

A Second-Order Upwind Least-Squares Scheme for Incompressible Flows on Unstructured Hybrid Grids

“…In symbols we have (4) where u; is the velocity component normal to the face i E aT and acf>/ an is the derivative in the (exterior) normal direction to the face, that is, acf>/an '" grad cf> . n.…”

“…Finite-volume computations using unstructured grids are used largely in the context of compressible flows; see, e.g., [2][3][4][5][6]. Hybrid triangular/quadrilateral grids have been employed in compressible flow calculations; see, e.g., [7], where the quadrilaterals are stretched directionally in the flow regions having one-dimensional features.…”