Aldo Bonfiglioli

Fluctuation Splitting Schemes for the Compressible and Incompressible Euler and Navier-Stokes Equations

Introduced in the late eighties by Roe, fluctuation splitting (or residual distribution) schemes have recently emerged as a viable alternative to Finite Volume and Finite Element methods for PDE based, fluid dynamics simulations using unstructured meshes. Their application to the numerical approximation of the compressible and incompressible Euler and Navier-Stokes equations is described, emphasizing low Mach number and incompressible applications. The advantages provided by time-preconditioning techniques are discussed and details of the implementation are given.

Shock interaction computations on unstructured, two-dimensional grids using a shock-fitting technique

A new shock-fitting technique has been recently proposed and implemented by the authors in conjunction with an unstructured shock-capturing solver. In the present paper, the attention is addressed towards the computation of shock-shock and shock-wall interactions by means of this novel computational technique.

Convergence Analysis of Shock-Capturing and Shock-Fitting Solutions on Unstructured Grids

A new shock-fitting technique for unstructured two- and three-dimensional meshes has been recently proposed and developed by the authors. In the present paper, both global and local a posteriori grid-convergence analysis is used to quantitatively measure the discretization error and order of convergence of the numerical solutions obtained using this new unstructured shock-fitting technique. Specifically, the analysis has considered the numerical solutions of two different flows characterized by the presence of strong shocks: a transonic source flow and an hypersonic flow past a circular cylinder. It is shown that the shock-fitting technique allows to compute numerical solutions that converge, both pointwise and in a global sense, with an observed order of accuracy that is very close to the design order of the spatial discretization scheme and with very small discretization errors.

An Implicit Fluctuation Splitting Scheme for Turbomachinery Flows

This paper describes an accurate, robust and efficient methodology for solving two-dimensional steady transonic turbomachinery flows. The Euler fluxes are discretized in space using a hybrid multidimensional upwind method, which, according to the local flow conditions, uses the most suitable fluctuation splitting (FS) scheme at each cell of the computational domain. The viscous terms are discretized using a standard Galerkin finite element scheme. The eddy viscosity is evaluated by means of the Spalart-Allmaras turbulence transport equation, which is discretized in space by means of a mixed FS-Galerkin approach. The equations are discretized in time using an implicit Euler scheme, the Jacobian being evaluated by two-point backward differences. The resulting large sparse linear systems are solved sequentially using a preconditioned GMRES strategy. The proposed methodology is employed to compute subsonic and transonic turbulent flows inside a high-turning turbine-rotor cascade.

RANS simulations of a junction flow

The ERCOFTAC junction flow is numerically simulated with both a structured and an unstructured RANS solver for incompressible flows. The structured code adopts a finite volume, cell-centered formulation while the unstructured code uses residual distribution schemes and a vertex centered storage of the unknowns. Two differential eddy viscosity models, based on local quantities, are considered in the computations: the one-equation Spalart–Allmaras model and the two equations model proposed by Lam and Bremhorst. The grid dependence of the numerical solutions is evaluated by means of a convergence analysis based on computation of the GCI and a code-to-code comparison. The numerical results provided by both turbulence models are compared with the experimental measurements of the pressure and velocity fields.

An unstructured shock-fitting solver for hypersonic plasma flows in chemical non-equilibrium

Abstract A CFD solver, using Residual Distribution Schemes on unstructured grids, has been extended to deal with inviscid chemical non-equilibrium flows. The conservative equations have been coupled with a kinetic model for argon plasma which includes the argon metastable state as independent species, taking into account electron–atom and atom–atom processes. Results in the case of an hypersonic flow around an infinite cylinder, obtained by using both shock-capturing and shock-fitting approaches, show higher accuracy of the shock-fitting approach.

A mass-matrix formulation of unsteady fluctuation splitting schemes consistent with Roe’s parameter vector

A mass-matrix formulation of the fluctuation splitting schemes for solving compressible, unsteady flows is proposed. This formulation is consistent with the conservative linearisation based on parameter vector and allows to extend to unsteady flows the ‘invariance under similarity transformations’ property that had been shown to hold for the steady version of the schemes. Second-order time accuracy is achieved using a Petrov–Galerkin finite element interpretation of the fluctuation splitting schemes. The approach may however be readily applicable to all other time-accurate fluctuation splitting formulations that have been so far proposed in the literature. Applications of the proposed methodology to two- and three-dimensional, inviscid and viscous compressible flows are reported and discussed in the paper.

Shock-Fitting Versus Shock-Capturing Modeling of Strong Shocks in Nonequilibrium Plasmas

In this paper, a supersonic flow of an argon plasma around a cylinder has been investigated comparing shock fitting and shock capturing techniques. Shock-capturing codes are algorithmically simple, but are plagued by a number of numerical troubles, particularly evident when the shocks are strong and the grids unstructured. On the other hand, shock-fitting algorithms allow to accurately compute solutions on coarse meshes, but tend to be algorithmically complex. The kinetic scheme adopted includes the argon metastable state as an independent species and takes into account for electron-atom and atom-atom processes. Electron density distributions have been reported.

The role of mesh generation, adaptation, and refinement on the computation of flows featuring strong shocks

Within a continuum framework, flows featuring shock waves can be modelled by means of either shock capturing or shock fitting. Shock-capturing codes are algorithmically simple, but are plagued by a number of numerical troubles, particularly evident when shocks are strong and the grids unstructured. On the other hand, shock-fitting algorithms on structured grids allow to accurately compute solutions on coarse meshes, but tend to be algorithmically complex. We show how recent advances in computational mesh generation allow to relieve some of the difficulties encountered by shock capturing and contribute towards making shock fitting on unstructured meshes a versatile technique.

Numerical simulation of hypersonic flows past three-dimensional blunt bodies through a unstructured shock-fitting solver

Owing to the maturity nowadays reached by computational geometry, shock-fitting, i.e. treating shock waves as true surfaces of discontinuity may no longer be prohibitively complex, as commonly believed by CFD practitioners. In this paper we report on some newly implemented features and algorithmic improvements of an unstructured, shock-fitting algorithm for threedimensional flows that has been recently proposed by the authors. The shock wave is described using a double-sided triangulated surface which is allowed to float over a background tetrahedral grid while obeying to the Rankine-Hugoniot jump relations. A constrained, Delaunay tetrahedralization is applied in the neighbourhood of the shock-front to make sure that the triangular faces that make up the shock surface are part of the tetrahedral mesh that covers the entire computational domain. A shockcapturing, vertex-centred solver is used to discretise the governing PDEs ∗Associate Professor, AIAA member †Post-doctoral research assistant ‡Associate Professor, AIAA member §Professor ¶Post-doctoral research assistant ‖Professor, AIAA member