Development and analysis of high-order vorticity confinement schemes

High-order extensions of the Vorticity Confinement (VC) method are developed for the accurate com- putation of vortical flows, following the VC2 conservative formulation of Steinhoff. First, a high-order formulation of VC is presented for the case of the linear transport equation for decoupled schemes in space and time. A spectral analysis shows that the new nonlinear schemes have improved dispersive and dissipative properties compared to their linear counterparts at all orders of accuracy. For the Euler and Navier–Stokes equations, the original VC method is extended to 3 rd - and 5 th -order of accuracy, with the goal of developing a VC formulation that maintains the vorticity preserving capability of the original 1 st -order method and is suitable for application to high-order numerical simulations. The high-order ex- tensions remain both independent of the choice of baseline numerical scheme and rotationally invariant since they are based on the Laplace operator. Numerical tests validate the increased order of accuracy, vorticity-preserving capability and compatibility of the VC extensions with high-order methods

Implicit large eddy simulation for unsteady multi-component compressible turbulent flows

Numerical methods for the simulation of shock-induced turbulent mixing have been investigated, focussing on Implicit Large Eddy Simulation. Shock-induced turbulent mixing is of particular importance for many astrophysical phenomena, inertial confinement fusion, and mixing in supersonic combustion. These disciplines are particularly reliant on numerical simulation, as the extreme nature of the flow in question makes gathering accurate experimental data difficult or impossible. A detailed quantitative study of homogeneous decaying turbulence demonstrates that existing state of the art methods represent the growth of turbulent structures and the decay of turbulent kinetic energy to a reasonable degree of accuracy. However, a key observation is that the numerical methods are too dissipative at high wavenumbers (short wavelengths relative to the grid spacing). A theoretical analysis of the dissipation of kinetic energy in low Mach number flows shows that the leading order dissipation rate for Godunov-type schemes is proportional to the speed of sound and the velocity jump across the cell interface squared. This shows that the dissipation of Godunov-type schemes becomes large for low Mach flow features, hence impeding the development of fluid instabilities, and causing overly dissipative turbulent kinetic energy spectra. It is shown that this leading order term can be removed by locally modifying the reconstruction of the velocity components. As the modification is local, it allows the accurate simulation of mixed compressible/incompressible flows without changing the formulation of the governing equations. In principle, the modification is applicable to any finite volume compressible method which includes a reconstruction stage. Extensive numerical tests show great improvements in performance at low Mach compared to the standard scheme, significantly improving turbulent kinetic energy spectra, and giving the correct Mach squared scaling of pressure and density variations down to Mach 10−4. The proposed modification does not significantly affect the shock capturing ability of the numerical scheme. The modified numerical method is validated through simulations of compressible, deep, open cavity flow where excellent results are gained with minimal modelling effort. Simulations of single and multimode Richtmyer-Meshkov instability show that the modification gives equivalent results to the standard scheme at twice the grid resolution in each direction. This is equivalent to sixteen times decrease in computational time for a given quality of results. Finally, simulations of a shock-induced turbulent mixing experiment show excellent qualitative agreement with available experimental data

Parametric Study of Decay of Homogeneous Isotropic Turbulence Using Large Eddy Simulation

Numerical simulations of decaying homogeneous isotropic turbulence are performed with both low-order and high-order spatial discretization schemes. The turbulent Mach and Reynolds numbers for the simulations are 0.2 and 250, respectively. For the low-order schemes we use either second-order central or third-order upwind biased differencing. For higher order approximations we apply weighted essentially non-oscillatory (WENO) schemes, both with linear and nonlinear weights. There are two objectives in this preliminary effort to investigate possible schemes for large eddy simulation (LES). One is to explore the capability of a widely used low-order computational fluid dynamics (CFD) code to perform LES computations. The other is to determine the effect of higher order accuracy (fifth, seventh, and ninth order) achieved with high-order upwind biased WENO-based schemes. Turbulence statistics, such as kinetic energy, dissipation, and skewness, along with the energy spectra from simulations of the decaying turbulence problem are used to assess and compare the various numerical schemes. In addition, results from the best performing schemes are compared with those from a spectral scheme. The effects of grid density, ranging from 32 cubed to 192 cubed, on the computations are also examined. The fifth-order WENO-based scheme is found to be too dissipative, especially on the coarser grids. However, with the seventh-order and ninth-order WENO-based schemes we observe a significant improvement in accuracy relative to the lower order LES schemes, as revealed by the computed peak in the energy dissipation and by the energy spectrum

A mesh transparent numerical method for large-eddy simulation of compressible turbulent flows

A Large Eddy-Simulation code, based on a mesh transparent algorithm, for hybrid unstructured meshes is presented to deal with complex geometries that are often found in engineering flow problems. While tetrahedral elements are very effective in dealing with complex geometry, excessive numerical diffusion often affects results. Thus, prismatic or hexahedral elements are preferable in regions where turbulence structures are important. A second order reconstruction methodology is used since an investigation of a higher order method based upon Lele's compact scheme has shown this to be impractical on general unstructured meshes. The convective fluxes are treated with the Roe scheme that has been modified by introducing a variable scaling to the dissipation matrix to obtain a nearly second order accurate centred scheme in statistically smooth flow, whilst retaining the high resolution TVD behaviour across a shock discontinuity. The code has been parallelised using MPI to ensure portability. The base numerical scheme has been validated for steady flow computations over complex geometries using inviscid and RANS forms of the governing equations. The extension of the numerical scheme to unsteady turbulent flows and the complete LES code have been validated for the interaction of a shock with a laminar mixing layer, a Mach 0.9 turbulent round jet and a fully developed turbulent pipe flow. The mixing layer and round jet computations indicate that, for similar mesh resolution of the shear layer, the present code exhibits results comparable to previously published work using a higher order scheme on a structured mesh. The unstructured meshes have a significantly smaller total number of nodes since tetrahedral elements are used to fill to the far field region. The pipe flow results show that the present code is capable of producing the correct flow features. Finally, the code has been applied to the LES computation of the impingement of a highly under-expanded jet that produces plate shock oscillation. Comparison with other workers' experiments indicates good qualitative agreement for the major features of the flow. However, in this preliminary computation the computed frequency is somewhat lower than that of experimental measurements.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A coupled implicit-explicit time integration method for compressible unsteady flows

This paper addresses how two time integration schemes, the Heun's scheme for explicit time integration and the second-order Crank-Nicolson scheme for implicit time integration, can be coupled spatially. This coupling is the prerequisite to perform a coupled Large Eddy Simulation / Reynolds Averaged Navier-Stokes computation in an industrial context, using the implicit time procedure for the boundary layer (RANS) and the explicit time integration procedure in the LES region. The coupling procedure is designed in order to switch from explicit to implicit time integrations as fast as possible, while maintaining stability. After introducing the different schemes, the paper presents the initial coupling procedure adapted from a published reference and shows that it can amplify some numerical waves. An alternative procedure, studied in a coupled time/space framework, is shown to be stable and with spectral properties in agreement with the requirements of industrial applications. The coupling technique is validated with standard test cases, ranging from one-dimensional to three-dimensional flows

Homogeenisen seosmallin verifiointi vapaan nestepinnan ongelmaan

In this thesis, the applicability of the homogeneous mixture model of Finflo for the free surface problem is studied. The free surface problem is fundamental in marine hydrodynamics, and a special case in two phase flows. The work explores the basis of this type of modelling from mathematical and numerical viewpoint, and verifies the mixture model for the problem. The mathematical background of the problem is presented, together with the nature of it from the perspective of marine hydrodynamics. The bulk flow equations are usually averaged conditionally such that the governing equations of the multiphase model are formally the same as in the case of single phase flow. It can be shown that one additional equation suffices for the description of the segregated phases. Here, the convection equation of the void fraction is utilized. The void fraction equation is derived in conservative form based on the incompressibility constraint of the individual phases. The convection of the void fraction corresponds to the so-called Riemann problem. This is studied thoroughly by developing a two-dimensional solver for the comparison of some well-known schemes for the spatial discretisation of the convective quantity. This solver is applied to the convection of a discontinuous distribution of the void fraction. In addition, the so-called SUPERBEE limiter is implemented to the Finflo code for the extrapolation of the convective void fraction. The numerical solution of the Navier-Stokes equations for simulations of two phase flows is covered comprehensively. The code Yaffa, developed at the Aalto University, has a modern VOF model implemented, and for this reason, it is here used as a reference code. The solution algorithms, the computation of the convective quantities, the pressure correction stages as well as the treatment of the segregated phases in both of the codes are discussed in detail. The two phase flow over a submerged ground elevation is computed using the codes Finflo and Yaffa, and the forming free surface wave is compared to those found from the literature. The aim of this thesis is to get acquainted with the nature of the problem in conjunction with the specific methodology used to solve such flows. This is done in order to understand the requirements and possible modifications needed for the model when we wish to accurately predict ship flow phenomena that are not solvable using the traditional free surface tracking strategies. This way, the verification of the mixture model of Finflo is achieved.Tässä työssä tutkitaan Finflon homogeenisen seosmallin soveltuvuutta vapaan nestepinnan ongelmaan. Vapaan nestepinnan ongelma on keskeinen laivahydrodynamiikassa, ja samalla monifaasivirtauksien erikoistapaus. Työssä perehdytään tällaisen mallinnuksen perusteisiin matemaattisessa ja numeerisessa mielessä, ja verifioidaan samalla seosmallia tälle ongelmalle. Työssä esitetään ongelman matemaattinen tausta sekä sen luonne laivahydrodynamiikan kannalta. Virtausta kuvaavat yhtälöt yleensä keskiarvostetaan ehdollisesti se. käytettävän monifaasimallin perusyhtälöt ovat muodollisesti samat, kuin yksifaasisessakin tapauksessa. Voidaan osoittaa, että tässä tapauksessa erillisten faasien kuvaukseen riittää yksi lisäyhtälö, joksi työssä otetaan aukko-osuuden konvektioyhtälö. Aukko-osuusyhtälö johdetaan säilymismuodossa perustuen faasien kokoonpuristumattomuusoletukseen. Mainittu lisäyhtälö vastaa luonteeltaan konvektioyhtälön ns. Riemann-probleemaa, ja tätä käsitellään perusteellisesti. Työssä kehitetään kaksidimensioinen ratkaisija, jolla vertaillaan tunnettuja menetelmiä konvektoituvan suureen paikkadiskretoinnille soveltamalla sitä epäjatkuvan aukko-osuusjakauman konvektioprobleemalle. Lisäksi implementoidaan Finfloon ns. SUPERBEE-rajoitin konvektoituvan aukko-osuuden ekstrapolointiin. Työssä käsitellään kattavasti Navier-Stokes -yhtälöiden numeerista ratkaisua kaksifaasivirtausimulointimenetelmien kannalta. Referenssikoodiksi otetaan Aalto-yliopistossa kehitetty Yaffa, johon nykyaikainen VOF-malli on implementoitu. Muiden muassa koodien ratkaisualgoritmi, konvektoituvien suureiden laskenta, painekorjausvaihe sekä erottuneiden faasien käsittely kuvataan perusteellisesti. Finflo- ja Yaffa -koodeilla lasketaan kaksifaasivirtaus vedenalaisen kummun yli, ja syntynyttä aaltokuviota verrataan myös kirjallisuudesta löytyviin tuloksiin. Työn ajatuksena on tutustua vapaan nestepinnan ongelman luonteeseen yhdessä tällaisen yleisemmän ratkaisutavan kanssa. Tavoitteena on ymmärtää mallille asetettavia vaatimuksia sekä sitä, millaisia modifikaatioita siihen tulisi tehdä, kun esim. pyritään ennustamaan tarkasti sellaisia laivavirtauksiin liittyviä ilmiöitä, joihin perinteiset pintaa seuraavat mallit eivät pysty. Tällä tavalla saatiin Finflon seosmallin verifiointi aikaiseksi

Richtmyer-Meshkov instability with reshock and particle interactions

Richtmyer-Meshkov instability (RMI) occurs when an interface of two fluids with different densities is impulsively accelerated. The main interest in RMI is to understand the growth of perturbations, and numerous theoretical models have been developed and validated against experimental/numerical studies. However, most of the studies assume very simple initial conditions. Recently, more complex RMI has been studied, and this study focuses on two cases: reshocked RMI and multiphase RMI. It is well known that reshock to the species interface causes rapid growth of interface perturbation amplitude. However, the growth rates after reshock are not well understood, and there are no practical theoretical models yet due to its complex interface conditions at reshock. A couple of empirical expressions have been derived from experimental and numerical studies, but these models are limited to certain interface conditions. This study performs parametric numerical studies on various interface conditions, and the empirical models on the reshocked RMI are derived for each case. It is shown that the empirical models can be applied to a wide range of initial conditions by choosing appropriate values of the coefficient. The second part of the study analyzes the flow physics of multiphase RMI. The linear growth model for multiphase RMI is derived, and it is shown that the growth rates depend on two nondimensional parameters: the mass loading of the particles and the Stokes number. The model is compared to the numerical predictions under two types of conditions: a shock wave hitting (1) a perturbed species interface surrounded by particles, and (2) a perturbed particle cloud. In the first type of the problem, the growth rates obtained by the numerical simulations are in agreement with the multiphase RMI growth model when Stokes number is small. However, when the Stokes number is very large, the RMI motion follows the single-phase RMI growth model since the particle do not rapidly respond while the RMI instability grows. The second type of study also shows that the multiphase RMI model is applicable if Stokes number is small. Since the particles themselves characterize the interface, the range of applicable Stokes number is smaller than the first study. If the Stokes number is in the order of one or larger, the interface experiences continuous acceleration and shows the growth profile similar to a Rayleigh-Taylor instability.M.S.Committee Chair: Menon, Suresh; Committee Member: Sankar, Lakshmi; Committee Member: Yang, Vigo

Coupling of time integration schemes for compressible unsteady flows

This work deals with the design of a hybrid time integrator that couples spatially explicit and implicit time integrators. In order to cope with the industrial solver of Ariane Group called FLUSEPA, the explicit scheme of Heun and the implicit scheme of Crank-Nicolson are hybridized using the transition parameter : the whole technique is called AION time integration. The latter is studied into details with special focus on spectral behaviour and on its ability to keep the accuracy. It is shown that the hybrid technique has interesting dissipation and dispersion properties while maintaining precision and avoiding spurious waves. Moreover, this hybrid approach is validated on several academic test cases for both convective and diffusive fluxes. And as expected the method is more interesting in term of computational time than standard time integrators. For the extension of this hybrid approach to the temporal adaptive method implemented in FLUSEPA, it was necessary to improve some treatments in order to maintain conservation and acceptable spectral properties. Finally the hybrid time integration was also applied to a RANS/LES turbulent test case with interesting computational time while capturing the flow physics