Efficient p‐multigrid discontinuous Galerkin solver for complex viscous flows on stretched grids

A simple distribution function-based gas-kinetic scheme for simulation of viscous incompressible and compressible flows

A high-order accurate unstructured spectral difference lattice Boltzmann method for computing inviscid and viscous compressible flows

We present a study of the effectiveness of asynchronous incomplete LU factorization preconditioners for the time-implicit solution of compressible flow problems while exploiting thread-parallelism within a compute node. A block variant of the asynchronous fine-grained parallel preconditioner adapted to a finite volume discretization of the compressible Navier--Stokes equations on unstructured grids is presented, and convergence theory is extended to the new variant. Experimental (numerical) results on the performance of these preconditioners on inviscid and viscous laminar two-dimensional steady-state test cases are reported. It is found, for these compressible flow problems, that the block variant performs much better in terms of convergence, parallel scalability, and reliability than the original scalar asynchronous ILU preconditioner. For viscous flow, it is found that the ordering of unknowns may determine the success or failure of asynchronous block-ILU preconditioning, and an ordering of grid cells suitable for solving viscous problems is presented.

A multigrid scheme has been developed for the acceleration of the solution of compressible inviscid and viscous flow problems. A higher order accurate upwind conservative finite volume scheme has been used for the discretization of the Euler and the Reynolds-Averaged Navier-Stokes equations. For the multigrid implementation, the “alternative point of view” of the Full Approximation scheme has been employed together with a conservative restriction operator to maintain the fine grid accuracy. The present multigrid scheme has been designed to take full advantage of the implicit unfactored solution scheme of the single grid code by introducing an alternative multigrid V-cycle. The proposed method attains up to 25-fold acceleration with respect to the single grid solution for moderate size grids. Moreover, the results demonstrate that the computational time increases proportional to the number of volumes when global refinements are applied so, the present multigrid scheme is very favorable for large scale computations.

An evaluation of cell type finite difference methods for solving viscous flow problems

The work focuses on the development of a 2D quadrilateral element based Spectral Difference solver for viscous flow calculations, and the application of the p-multigrid method and implicit time-stepping to accelerate convergence. This paper extends the previous work by Liang et al (2009) on the p-multigrid method for 2D inviscid compressible flow, to viscous flows. The high-order spectral difference solver for unstructured quadrilateral meshes is based on the formulation of Sun et al for unstructured hexahedral elements. The p-multigrid method operates on a sequence of solution approximations of different polynomial orders ranging from one upto four. An efficient preconditioned Lower-Upper Symmetric Gauss-Seidel (LU-SGS) implicit scheme is also implemented. The spectral difference method is applied to a variety of inviscid and viscous compressible flow problems. The speed-up using the p-Multigrid and Implicit time-stepping techniques is also demonstrated.

High fidelity field simulations using density and pressure based approaches

Zonal disturbance region update method for steady compressible viscous flows

Due to its attractive properties in computing compressible flows, such as sharp capturing of discontinuities, satisfying entropy condition and positivity preservation, the HLLEM approximate Riemann solver has been widely applied for simulations of many compressible flow problems. However, when it comes to weakly compressible or incompressible flows, the HLLEM scheme cannot give physically correct solutions. In the current study, a simple low Mach number fix is applied to improve the accuracy and stability of HLLEM approximate Riemann solver in the low Mach limit. As a result, a modified HLLEM scheme called LM-HLLEM scheme is proposed. Numerical results demonstrate that the proposed LM-HLLEM scheme is able to compute various flow problems accurately and robustly ranging from compressible to low Mach incompressible flows.

A new technique is developed for computations of compressible, viscous flow over multiple-bodies. In this scheme, an implicit finite-difference method(FDM) is applied regions of near-bodies with body-fitted grids, and those FDM-regions are patched by solving the remaining regions using an explicit finite-element method (FEM). With this zonal approach, the computational efficiency and the solution quality of FDM are retained, while the geometric flexibility is given by the FEM. The most important advantage the present technique yields is that the flow solver with this FDM-FEM zonal approach can be applied d various kinds of multiple-body flow fields without modifying the basic solution procedure. Several test problems are computed by the method in order d validate the capabilities of the FDM-FEM zonal approach for compressible viscous flows over multiple-bodies.

An implicit scheme for the time accurate solution of three dimensional compressible fluid flow problems with moving boundaries on unstructured tetrahedral meshes is described. The numerical scheme is nominally second order accurate in both space and time and satisfies a geometric conservation law. For improved computational performance, the implicit equation system is solved by explicit iteration with multigrid acceleration. For the multigrid implementation, the coarse meshes are automatically generated by an agglomeration technique. The change in the solution domain geometry with time is handled by moving the mesh using a spring analogy scheme, with local remeshing performed in regions of reduced mesh quality. Copyright © 2003 John Wiley & Sons, Ltd.

(English) This thesis deals with finite element methods to solve compressible flow problems, an important branch of Computational Fluid Dynamics (CFD) whose applications are widespread in many areas of engineering and science. In spite of the increasing amount of computational resources made available for the scientific and engineering research communities, the numerical simulation of complex compressible phenomena in many practical applications is still a challenge. These type of flow problems are extremely demanding in what concerns numerical computations and memory requirements. In particular, in this thesis we investigate the possibility to solve the underlying algebraic systems in a decoupled manner, a technique usually called fractional step or segregation method. Although segregation techniques have been broadly studied and analyzed for the incompressible Navier-Stokes equations, allowing for the separate resolution of velocity and pressure unkonwns, much less has been explored for compressible problems. The interest on this type of technique not only comes from the fact that it permits a segregated calculation of the problem unkonwns (usually leading to better conditioned systems) but from the associated reduction of the computational cost. We study three different problems inside the compressible CFD research branch in separated chapters: the isentropic Navier-Stokes equations, the Navier-Stokes problem written in primitive variables (velocity, pressure and temperature), and the navier-Stokes problem written in the classical formulation with conservative variables (momentum, density, total energy). For each of these problems, first we propose a finite element stabilized formulation framed within the Variational MultiScale concept, which allows to use equal interpolation spaces for all the variables in play. Second, and once space and time discretizations are selected, we derive fractional step methods up to second order in time. Finally, all the schemes are implemented in a parallel multiphysics code and representative simulations are carried out in order to analyze the performance of the proposed techniques. (Español) Esta tesis se centra en la aplicación del método de elementos finitos a problemas de flujo compresible, unas de las ramas más importantes dentro de la mecánica de fluidos computacional (CFD, por sus siglas en inglés), y cuya aplicación es amplia en distintas áreas de ciencia e ingeniería. A pesar del aumento de los recursos computacionales que se ponen a disposición de la comunidad científica, la solución numérica de problemas complejos de flujo compresible para distintas aplicaciones prácticas es aún un reto. Este tipo de problemas de flujo son extremadamente exigentes en lo que se refiere al cálculo numérico y los requisitos de memoria computacionales. En particular, en esta tesis se estudia la posibilidad de resolver los sistemas algebraicos que subyacen tras la aplicación del método de elementos finitos de una forma desacoplada, una técnica que usualmente se denomina de paso fraccionado o método de segregación. Aunque las técnicas de segregación han sido ampliamente estudiadas y analizadas para el problema incompresible de Navier-Stokes, lo que permite un cálculo separado de las variables velocidad y presión, poco se ha explorado su aplicación a problemas de flujo compresible. El interés en este tipo de técnicas radica no solo en el hecho de que permite un cálculo segregado de las incógnitas del problema (generalmente dando lugar además a sistemas algebraicos mejor condicionados), sino también en la reducción de coste computacional que ofrecen. Se estudian tres problemas distintos dentro de la rama de investigación en CFD de flujos compresibles: las ecuaciones isentrópicas de Navier-Stokes, el problema compresible de Navier-Stokes escrito en variables primitivas (velocidad, presión y temperatura) y el problema compresible de Navier-Stokes planteado de manera clásica en variables conservativas (momento, densidad y energía total). Para cada uno de estos casos, primero se propone una formulación de elementos finitos, estabilizada bajo el marco de trabajo de las multiescalas variacionales (VMS, por sus siglas en inglés), lo que en la práctica permite utilizar la misma interpolación para las variables del problema. En segundo lugar, y una vez las discretizaciones en tiempo y espacio han sido seleccionadas, se proponen métodos de paso fraccionado para cada problema de hasta segundo orden en tiempo. Finalmente, todos los algoritmos se implementan en una plataforma de código paralelo para problemas multifísicos y se llevan a cabo simulaciones representativas con el fin de analizar el rendimiento de las técnicas propuestas.

An efficient formulation for the robust design optimization of compressible fluid flow problems is presented. The methodology has three essential ingredients: a highly accurate flow solver, robust and efficient design sensitivities from a discrete adjoint formulation based on a dissipative flow solver and progressive optimization, whereby a sequence of operations, containing a partially converged flow solution, followed by an adjoint solution followed by an optimization step is performed. Furthermore, the progressive optimization involves the use of progressively finer grids. The methodology is shown to be accurate, robust and highly efficient, with a converged design optimization produced in no more than the amount of computational work to perform from one to three flow analyses.Key WordsAirfoilInverse DesignDirect DesignEuler Flow

Commonly, for the simulation of cavitation in centrifugal pumps incompressible flow solvers with VOF kind cavitation models are applied. Since the source/sink terms of the void fraction transport equation are based on simplified bubble dynamics, empirical parameters may need to be adjusted to the particular pump operating point. In the present study a barotropic cavitation model, which is based solely on thermodynamic fluid properties and does not include any empirical parameters, is applied on a single flow channel of a pump impeller in combination with a time-explicit viscous compressible flow solver. The suction head curves (head drop) are compared to the results of an incompressible implicit standard industrial CFD tool and are predicted qualitatively correct by the barotropic model.

This thesis investigates the flexibility associated to Discontinuous Galerkin (DG) discretization on very general meshes obtained by means of agglomeration techniques. The work begins with a brief overview of the main tools that have been extended or specifically developed to deal with arbitrarily shaped elements in the DG context. Then two different implementations of the BRMPS scheme introduced by Bassi, Rebay, Mariotti, Pedinotti and Savini in [16] for the DG discretization of the Laplace operator on arbitrarily shaped elements have been presented. The validation of the scheme on a Poisson problem shows that the discrete polynomial space preserves optimal convergence properties. The discretization of the second order differential operator has been directly extended to the Navier-Stokes equations and the Reynolds Averaged Navier-Stokes (RANS) equations coupled with the k-w turbulence model of Wilcox [54]. In this regard, an implicit time integration strategy has been considered and assessed on classical validation test cases for the compressible f uid dynamics. Then a simple alternative approach to high-order mesh generation is presented. Indeed, once a standard fine grid able to provide an accurate domain discretization has been produced by means of standard low-order grid generation tools, a computational mesh suitable for the desired accuracy and computationally affordable can be obtained via agglomeration while keeping the boundary resolution of the fine grid. The effectiveness of this approach in representing the geometry of the domain is numerically assessed both on a Poisson model problem and on challenging inviscid and viscous test cases. Finally, the freedom in simply defining the topology of agglomerated meshes leads to a nonstandard approach to h-adaptivity that exploits adaptive agglomeration coarsening of a properly fine underlying grid. The effectiveness of this approach has been assessed on test cases involving both error-based and fl ow feature-based simple estimators.