A third-order finite-volume residual-based scheme for the 2D Euler equations on unstructured grids

A residual-based (RB) scheme relies on the vanishing of residual at the steady-state to design a transient first-order dissipation, which becomes high-order at steady-state. Initially designed within a finite-difference framework for computations of compressible flows on structured grids, the RB schemes displayed good convergence, accuracy and shock-capturing properties which motivated their extension to unstructured grids using a finite volume (FV) method. A second-order formulation of the FV–RB scheme for compressible flows on general unstructured grids was presented in a previous paper. The present paper describes the derivation of a third-order FV–RB scheme and its application to hyperbolic model problems as well as subsonic, transonic and supersonic internal and external inviscid flows.     

Simulation of the flow past a circular cylinder in the supercritical regime by blending RANS and variational-multiscale LES models

A strategy which blends a variational multiscale large eddy simulation (VMS-LES) model and a RANS model in a hybrid approach is investigated. A smooth blending function, which is based on the value of a blending parameter, is used for switching from VMS-LES to RANS. Different definitions of the blending parameter are investigated. The capabilities of the novel hybrid approach are appraised in the simulation of the flow around a circular cylinder at a Reynolds number 1.4×10⁵, based on the freestream velocity and on the cylinder diameter, in the presence of turbulent boundary-layer due to turbulent inflow conditions. A second study at Reynolds numbers from Re=6.7×10⁵ to 1.25×10⁶ is also presented. The effect of using the VMS-LES approach in the hybrid model is evaluated. Results are compared to those of other RANS, LES and hybrid simulations in the literature and with experimental data     

The adaptation of unstructured grids for transonic viscous flow simulation

The computation of viscous flows using unstructured grids is a relatively new area of research. This paper details work carried out to analyse the efficiency of initial unstructured viscous grids and their adaptation, particularly in the region of aerofoil trailing edges. This will enable an optimal approach to be established which can be extended into practical three-dimensional viscous flow simulations.     

Large eddy simulation of cross-flow through a staggered tube bundle at subcritical Reynolds number

The Large Eddy Simulation (LES) technique is used to study the vortex shedding characteristics inside a staggered tube array consisting of six rows with intermediate spacings (S_L/D×S_T/D=1.6×3.6) at the subcritical Reynolds number of 8600 (based on the gap velocity). The filtered equations are discretised using the finite volume method in an unstructured, collocated grid arrangement with second-order accurate methods in space and time. The predictions of mean velocities and Reynolds stresses are in very good agreement with detailed LDA measurements performed in 17 stations along the depth of the array. The sizes of the recirculation zones behind the cylinders in the first and third row also compare favourably with available correlations. Two distinct and independent shedding frequencies are detected behind the first two rows, but the high-frequency component vanishes in the downstream rows. The corresponding Strouhal numbers agree well with measurements available in the literature for similar tube spacings. The lift coefficient as well as instantaneous flow patterns of the whole array are also examined.     

Numerical investigation of inviscid shock wave dynamics in an expansion tube

Highly complicated shock wave dynamics has been numerically calculated by solving the Euler equations for a circular shock tube suddenly expanded three times of the original tube diameter atx=0. Shock waves of different shock Mach number,M _s =1.5 and 2.0, have produced remarkably distinct blast jet structures. A planar shock wave took its final form after the blast by repeated Mach reflections of the blast wave: the first one at the wall and the second one at the central axis. The central Mach disc overtook and merged with the annular Mach stem before the planar shock wave was formed. In contrast to the blast wave which would propagate spherically in an open space, the present blast wave undergoes complex morphological transformation in the restricted flow passage, resulting in an unstable and oscillatory blast jet structure of highly rotational nature. The slipstream tube emanating from the shock tube exit corner decomposed into a chain of small vortex rings that interacted with the barrel shock of the jet, which caused periodic collapse of the jet structure. The finite volume-FCT formulation equipped with the time-dependenth-refinement adaptive unstructured triangular mesh technique in the present paper has contributed to resolution of the intricate physical discontinuities developing in the blast flow fields.     

Hybrid Unsteady RANS and PDF Method for Turbulent Non-Reactive and Reactive Flows

A hybrid unsteady Reynolds-averaged numerical simulation (U-RANS) and probability density function (PDF) method is developed for turbulent non-reactive and reactive flows. The resulting modeled equations are solved by a consistent hybrid finite volume and Lagrangian Monte-Carlo particle method. Both turbulent non-reactive and reactive flows in a rectangular channel containing a triangular-shaped bluff-body are simulated. One-step and two-step mechanisms for propane/air combustion are used for the reactive case. The time-averaged results are compared with both experimental data and numerical results from the literature using large eddy simulation (LES) and steady RANS. The results of the present method are in good agreement with the experimental data, and they improve the numerical results available in the literature.     

Modified finite-volume method based on a cell vertex scheme for the solution of radiative transfer problems in complex 3D geometries

A modified finite-volume method based on a cell vertex scheme was applied to solve radiative transfer problems within a participating medium of complex three-dimensional shaped domain. The computational spatial domain of interest was divided into four-node tetrahedron elements with unstructured meshes while the adopted formulation was combined with a closure relation based on an exponential scheme. The studied medium was assumed to be grey, non-scattering and was bounded by black surfaces. Our results were then compared with those found in other articles on the subject. The approach shows a very good level of performance for wall heat transfer evaluation. Accurate results were obtained on coarse computational meshes and solution errors were found to decrease with grid refinement.     

Turbulent flow calculations using unstructured and adaptive meshes

A method of efficiently computing turbulent compressible flow over complex two-dimensional configurations is presented. The method makes use of fully unstructured meshes throughout the entire flow field, thus enabling the treatment of arbitrarily complex geometries and the use of adaptive meshing techniques throughout both viscous and inviscid regions of the flow field. Mesh generation is based on a locally mapped Delaunay technique in order to generate unstructured meshes with highly stretched elements in the viscous regions. The flow equations are discretized using a finite element Navier-Stokes solver, and rapid convergence to steady state is achieved using an unstructured multigrid algorithm. Turbulence modelling is performed using an inexpensive algebraic model, implemented for use on unstructured and adaptive meshes. Compressible turbulent flow solutions about multiple-element aerofoil geometries are computed and compared with experimental data.     

Algebraic turbulence models for the computation of two-dimensional high-speed flows using unstructured grids

The incorporation of algebraic turbulence models in a solver for the 2D compressible Navier–Stokes equations using triangular grids is described. A practical way to use the Cebeci–Smith model and to modify it in separated regions is proposed. The ability of the model to predict high-speed perfect-gas boundary layers is investigated from a numerical point of view.     

Modification of basis functions in high order discontinuous Galerkin schemes for advection equation

High order discontinuous Galerkin (DG) discretization schemes are considered for an advection boundary-value problem on 2-D unstructured grids with arbitrary geometry of grid cells. A number of test cases are developed to study the sensitivity of a high order DG scheme to local grid distortion. It will be demonstrated how to modify the formulation of a DG discretization for the advection equation. Our approach allows one to maintain the required accuracy on distorted grids while using a fewer number of basis functions for the solution approximation in order to save computational resources.