An embedded shock-fitting technique on unstructured dynamic grids

In this paper, a new shock-fitting technique based on unstructured dynamic grids is proposed to improve the performances of the unstructured “boundary” shock-fitting technique developed by Liu and co-workers in [1, 2]. The main feature of this new technique, which we call the “embedded” shock-fitting technique, is its capability to insert or remove shocks or parts thereof during the calculation. This capability is enabled by defining subsets of grid-points (mutually connected by lines) which behave as either “common”- or “shock”-points, shock-waves being made of an ordered collection of shock-points. Two different sets of flow variables, corresponding to the upstream and downstream sides of the shocks, are assigned to the shock-points, which may be switched to common- and back to shock-points, a feature that allows to vary the length of the existing shocks and/or make new shock-branches appear. This paper illustrates the algorithmic features of this new technique and presents the results obtained when simulating both steady and un-steady, two-dimensional flows

Extrapolated shock fitting for two-dimensional flows on structured grids

Over the years the development of structured-grid shock-fitting techniques faced two main problems: the handling of a moving discontinuity on a fixed background grid and the capability of simulating complex flow configurations. In the proposed work, the authors present a new shock-fitting technique for structured-grid solvers that is capable of overcoming the limitations that affected the different approaches originally developed. The technique presented here removes the tight link between grid topology and shock topology, which characterizes previous shock fitting as well as front tracking methods. This significantly simplifies their implementation and more importantly reduces the computational overhead related to these geometrical manipulations. Interacting discontinuities and shocks interacting with a solid boundary are discussed and analyzed. Finally, a quantitative investigation of the error reduction obtained with the approach proposed via a global grid convergence analysis is presented

A new computational technique for re-entry flow calculations based upon a shock-fitting technique for unstructured grids

An in-house developed, 2D/3D unstructured CFD solver has been extended to deal with a mixture of thermally perfect gases in chemical non-equilibrium. The Euler equations have been coupled with a state-to-state kinetic model for argon plasma. The spatial discretization uses compact stencil Residual Distribution Schemes and shock waves can be modelled using either shock-capturing or shock-fitting. Promising results have been obtained using the shock-fitting approach for a 2D hypersonic flow past the fore-body of a circular cylinder

An unstructured shock-fitting solver for two-dimensional flows

A new floating Shock-Fitting technique featuring the explicit computation of shocks by means of the Rankine-Hugoniot relations has been implemented on unstructured grids. This paper illustrates the algorithmic features of this orginal technique and the results obtained in the computation of the hypersonic flow past a circular cylinder and a Mach reflection

Simulation of Shock Boundary Layer Interaction Using Shock Fitting Technique

An unstructured, shock-fitting algorithm, originally developed to simulate Eulerian flows, has being further developed to make it capable of dealing with shock/boundary-layer interactions. This paper illustrates the algorithmic features of this technique and the results achieved in the computation of hypersonic flows past compression ramps

Unstructured Shock-Fitting Calculations of the Transonic Flow in a Gas Turbine Cascade

Even though shock-capturing techniques are the de-facto standard in the CFD simulation of turbo-machinery flows, the accurate estimation of shock-induced losses in transonic flows can be severely hindered by the numerical errors that are generated along a captured shock and convected downstream. Indeed, and despite their widespread use, shock-capturing techniques are known to be plagued by a number of drawbacks that are inherent to the numerical details of the shock-capturing process. In recent works, the authors have developed a novel shock fitting technique for unstructured grids that has been applied to the computation of transonic, supersonic and hypersonic flows in both two and three space dimensions. In this paper, the proposed technique is applied to two-dimensional, transonic flows around an isolated profile and in a gas turbine cascade. It is shown that the use of unstructured meshes allows to relieve most of the algorithmic difficulties that have contributed to the dismissal of the shock-fitting technique in the framework of structured meshes. Moreover, it is confirmed that, in contrast to shock-capturing, shock-fitting allows to obtain very accurate solution on coarse meshes

Numerical simulation of shock-shock interactions with an unstructured 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 interactions by means of this novel computing technique. Different computing approaches are considered and their performances are assessed through the computation of a type IV shock-shock interaction

Hypersonic Flow Computations on Unstructured Grids: Shock-Capturing vs Shock-Fitting Approach

Capturing strong shocks is a difficult task. It is also known that it leads to accuracy degradation in the entire region downstream of the captured shock wave. Things get even worst when unstructured grids are used. In this paper we try to assess whether these drawbacks may be circumvented by combining shock-fitting and unstructured grids. Achievements, current difficulties and un-solved problems are presented and discussed

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