A STEADY PSEUDO-COMPRESSIBILITY APPROACH BASED ON UNSTRUCTURED HYBRID FINITE VOLUME TECHNIQUES APPLIED TO TURBULENT PREMIXED FLAME PROPAGATION

A pseudo-compressibility method for zero Mach number turbulent reactive flows with heat release is combined with an unstructured finite volume hybrid grid scheme. The spatial discretization is based on an overlapped cell vertex approach. An infinite freely planar flame propagating into a turbulent medium of premixed reactants is considered as a test case. The recourse to a flamelet combustion modeling for which the reaction rate is quenched in a continuous way ensures the uniqueness of the turbulent flame propagation velocity. To integrate the final form of discretized governing equations, a three-stage hybrid time-stepping scheme is used and artificial dissipation terms are added to stabilize the convergence path towards the final steady solution. The results obtained with such a numerical procedure prove to be in good agreement with those reported in the literature on the very same flow geometry. Indeed, the flame structure as well as its propagation velocity are accurately predicted thus confirming the validity of the approach followed and demonstrating that such a numerical procedure will be a valuable tool to deal with complex reactive flow geometries

Unstructured mesh based models for incompressible turbulent flows

A development of high resolution NFT model for simulation of incompressible flows is presented. The model uses finite volume spatial discretisation with edge based data structure and operates on unstructured meshes with arbitrary shaped cells. The key features of the model include non-oscillatory advection scheme Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) and non-symmetric Krylov-subspace elliptic solver. The NFT MPDATA model integrates the Reynolds Average Navier Stokes (RANS) equations. The implementation of the Spalart-Allmaras one equations turbulence model extends the development further to turbulent flows. An efficient non-staggered mesh arrangement for pressure and velocity is employed and provides smooth solutions without a need of artificial dissipation. In contrast to commonly used schemes, a collocated arrangement for flow variables is possible as the stabilisation of the NFT MPDATA scheme arises naturally from the design of MPDATA. Other benefits of MPDATA include: second order accuracy, strict sign-preserving and full multidimensionality. The flexibility and robustness of the new approach is studied and validated for laminar and turbulent flows. Theoretical developments are supported by numerical testing. Successful quantitative and qualitative comparisons with the numerical and experimental results available from literature confirm the validity and accuracy of the NFT MPDATA scheme and open the avenue for its exploitation for engineering problems with complex geometries requiring flexible representation using unstructured meshes

The simulation of incompressible flow using the artificial compressibility method.

In this work an algorithm is developed for simulating incompressible steady flow on two and three-dimensional unstructured meshes. The Navier-Stokes equations are briefly reviewed as the basic governing equation for fluid flow. Using this set of equations, in the limit of incompressible flow, the problem of imposing the time independent continuity equation on the momentum equations arises. This difficulty can be removed by employing the Artificial Compressibility approach. This approach modifies the continuity equation by adding a pseudo pressure time derivative. This modification makes the set of equations well conditioned for numerical solution. If the set of modified equations is used for the solution of steady state problems, the added pressure derivative tends to zero and the set of equations reduces to the steady state incompressible Navier-Stokes equations. The cell-vertex finite volume method is employed for solving the modified equations on unstructured triangular and tetrahedral meshes. The principles of central difference space discretisation are described and the basic ideas behind adding artificial dissipation term are reviewed. A normalisation procedure for the computation of the artificial dissipation term is adopted. Two different formulations based upon a cell-vertex finite volume method and a Galerkin finite element method for the discretisation of the viscous terms on unstructured triangular meshes are employed in two and three dimensions. A modification to the finite volume formulation is introduced for improving accuracy on unstructured grids. The issues relating to multi-stage time stepping, boundary conditions and some techniques for increasing computational efficiency are described. A general review of several methods for generating regular and irregular unstructured triangular and tetrahedral meshes are presented. The proposed algorithm is validated by solving several inviscid and viscous two-dimensional test cases. Extension of the algorithm to three dimensions are studied by using some further benchmark examples. Some engineering applications are considered to present the ability of the developed flow solver to simulate more complicated real world problems. Finally, some conclusions are drawn and a few guidelines for further research work are suggested

Semiannual report

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period 1 Oct. 1994 - 31 Mar. 1995

[Activity of Institute for Computer Applications in Science and Engineering]

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science

Synthetic turbulence generation for high-order scale-resolving simulations on unstructured grids

An extended version of the synthetic eddy method for generation of synthetic turbulence has been developed via a source term formulation and implemented in the open-source cross-platform solver PyFR. The method caters for the full space-dependent anisotropy of the target turbulent length scales, and it is agnostic of the space and time discretization of the underlying solver, which can be incompressible or compressible. Moreover, the method does not require each solution point to communicate with nearest neighbors; thus, it is well suited for modern, massively parallel, high-order unstructured codes which support mixed and possibly curved elements. The method has been applied to two test cases: incompressible plane channel flow at Reτ 180 and compressible flow over an SD7003 aerofoil at Re 66;000, Ma 0.2, and α 4 deg. The channel flow case was run on three topologically different meshes composed of hexahedra, prisms, and a combination of prisms and tetrahedra, respectively. Almost identical results have been obtained on the three meshes. Results also show that taking into account the anisotropy of the turbulent length scales can reduce the development length. For the SD7003 aerofoil case, the injection of synthetic turbulence improves agreement between numerical and experimental results

Adaptive mesh simulations of compressible flows using stabilized formulations

This thesis investigates numerical methods that approximate the solution of compressible flow equations. The first part of the thesis is committed to studying the Variational Multi-Scale (VMS) finite element approximation of several compressible flow equations. In particular, the one-dimensional Burgers equation in the Fourier space, and the compressible Navier-Stokes equations written in both conservative and primitive variables are considered. The approximations made for the VMS formulation are extensively researched; the design of the matrix of stabilization parameters, the definition of the space where the subscales live, the inclusion of the temporal derivatives of the subscales, and the non-linear tracking of the subscales are formulated. Also, the addition of local artificial diffusion in the form of shock capturing techniques is included. The accuracy of the formulations is studied for several regimes of the compressible flow, from aeroacoustic flows at low Mach numbers to supersonic shocks. The second part of the thesis is devoted to make the solution of the smallest fluctuating scales of the compressible flow affordable. To this end, a novel algorithm for $h-$refinement of computational physics meshes in a distributed parallel setting, together with the solution of some refinement test cases in supercomputers are presented. The definition of an explicit a-posteriori error estimator that can be used in the adaptive mesh refinement simulations of compressible flows is also developed; the proposed methodology employs the variational subscales as a local error estimate that drives the mesh refinement. The numerical methods proposed in this thesis are capable to describe the high-frequency fluctuations of compressible flows, especially, the ones corresponding to complex aeroacoustic applications. Precisely, the direct simulation of the fricative [s] sound inside a realistic geometry of the human vocal tract is achieved at the end of the thesis.Esta tesis investiga métodos numéricos que aproximan la solución de las ecuaciones de flujo compresible. La primera parte de la tesis está dedicada al estudio de la aproximación numérica del flujo compresible por medio del método multiescala variacional (VMS) en elementos finitos. En particular, se consideran la ecuación de Burgers unidimensional descrita en el espacio de Fourier y las ecuaciones de Navier-Stokes de flujo compresible escritas en variables conservativas y primitivas. Las aproximaciones hechas para plantear la formulación VMS son ampliamente investigadas; el diseño de la matriz de parámetros de estabilización, la definición del espacio donde viven las subescalas, la inclusión de las derivadas temporales de las subescalas y el seguimiento no lineal de las subescalas son particularidades de la formulación que se analizan para cada una de las ecuaciones consideradas. Además, se incluye la adición de difusión artificial local en forma de técnicas de captura de choque. La precisión de las formulaciones se estudia para varios regímenes del flujo compresible, desde flujos aeroacústicos a bajos números de Mach hasta choques supersónicos. La segunda parte de la tesis está dedicada a hacer asequible la solución de las escalas fluctuantes más pequeñas del flujo compresible. Con este fin, se presenta un algoritmo novedoso para el refinamiento $h$ de las mallas de física computacional usadas en computación distribuida en paralelo. Además, se demuestra la solución en superordenadores de algunos casos de prueba del refinamiento de mallas. También se desarrolla la definición de un estimador de error explícito a posteriori que se puede usar en las simulaciones adaptativas de refinamiento de malla de flujos compresibles; la metodología propuesta emplea las subescalas variacionales como una estimación de error local que induce el refinamiento de la malla. Los métodos numéricos propuestos en esta tesis son capaces de describir las fluctuaciones de alta frecuencia de los flujos compresibles, especialmente los correspondientes a aplicaciones aeroacústicas complejas. Precisamente, la simulación directa del sonido consonántico fricativo [s] dentro de una geometría realista del tracto vocal humano se demuestra al final de la tesis

[Research activities in applied mathematics, fluid mechanics, and computer science]

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period April 1, 1995 through September 30, 1995

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required