Inviscid finite-volume lambda formulation

Abstract

A finite-volume lambda formulation for solving Euler equations and able to handle compressible as well as transonic flow computations is presented. The easy extension of the methodology to the solution of Navier-Stokes equations is indicated. The integration scheme is in nonconservative form in smooth flow regions in order to take advantage of its superior accuracy and computational efficiency. It automatically switches to conservative form in shock regions, in order to capture them correctly. Computations of two-and three-dimensional shockless source flows prove the superior accuracy and computational efficiency of the proposed technique in comparison with a classical conservative upwind methodology. Moreover, computed results referring to some two-and three-dimensional test cases are compared with numerical or experimental published ones, thus showing the capabilities of the proposed formulation to deal with inviscid subsonic as well as transonic flow cases.

Computations of viscous flows using a multigrid finite volume lambda formulation

“…The inviscid terms, on the contrary, are discretized according to the FVLF (Casalini and Dadone, 1993). The difference of the inviscid fluxes between two faces characterized by the same curvilinear direction can be written as:…”

“…As far as the second limitation is concerned, the present authors have suggested a finite volume lambda formulation (FVLF) (Casalini and Dadone, 1993) for a curvilinear frame of reference. In such a way the superior capabilities of finite volume techniques to compute three-dimensional flows in complex geometries can be fully exploited.…”

“…In such a way the superior capabilities of finite volume techniques to compute three-dimensional flows in complex geometries can be fully exploited. In Casalini and Dadone (1993), a hybrid technique has been also suggested in order to automatically capture discontinuities. The computed results have proven the methodology accuracy, the capability of capturing shocks correctly, and the ability to handle complex three-dimensional secondary flows.…”

On the numerical integration of multi‐dimensional, initial boundary value problems for the Euler equations in quasi‐linear form

“…As two-dimensional cases, we selected the flow through the Hobson 2 cascade, proposed in [34]. This supercritical solution can be obtained by hodograph transformation, and has been solved and discussed numerically in [35] and [36]. The Hobson 2 cascade prescribes a free-stream Mach number M ∞ = 0.575, a free-stream angle of attack θ ∞ = 46.123 that is the same as the angle at which the flow leaves the cascade, and a cascade solidity s = 1.9.…”

On the numerical integration of multi-dimensional, initial boundary value problems for the Euler equations in quasi-linear form

“…This supercritical solution can be obtained by hodograph transformation, and has been solved and discussed numerically in [35] and [36]. The Hobson 2 cascade prescribes a free-stream Mach number M ∞ = 0.575, a free-stream angle of attack θ ∞ = 46.123 that is the same as the angle at which the flow leaves the cascade, and a cascade solidity s = 1.9.…”