A novel SIMPLE-based pressure-enthalpy coupling scheme for engine flow problems

A novel method in CFD derived from the SIMPLE algorithm is presented. Instead of solving the linear equations for each variable and the pressurecorrection equation separately in a so-called segregated manner, it relies on the solution of a linear system that comprises the discretisation of enthalpy and pressurecorrection equation which are linked through physical coupling terms. These coupling terms reflect a more accurate approximation of the density update with respect to thermodynamics (compared to standard SIMPLE method). We show that the novel method is a reasonable extension of existing CFD techniques for variable density flows based on SIMPLE. The novel method leads to a reduction of the number of iterations of SIMPLE which translates in many – but not in all – cases to a reduction in computing time. We will therefore demonstrate practical advantages and restrictions in terms of computational efficiency for industrial CFD applications in the field of piston engine simulations

Efficient Solvers for Space-Time Discontinuous Galerkin Spectral Element Methods

In this thesis we study efficient solvers for space-time discontinuous Galerkin spectral element methods (DG-SEM). These discretizations result in fully implicit schemes of variable order in both spatial and temporal directions. The popularity of space-time DG methods has increased in recent years and entropy stable space-time DG-SEM have been constructed for conservation laws, making them interesting for these applications. The size of the nonlinear system resulting from differential equations discretized with space-time DG-SEM is dependent on the order of the method, and the corresponding Jacobian is of block form with dense blocks. Thus, the problem arises to efficiently solve these huge nonlinear systems with regards to CPU time as well as memory consumption. The lack of good solvers for three-dimensional DG applications has been identified as one of the major obstacles before high order methods can be adapted for industrial applications.It has been proven that DG-SEM in time and Lobatto IIIC Runge-Kutta methods are equivalent, in that both methods lead to the same discrete solution. This allows to implement space-time DG-SEM in two ways: Either as a full space-time system or by decoupling the temporal elements and using implicit time-stepping with Lobatto IIIC methods. We compare theoretical properties and discuss practical aspects of the respective implementations.When considering the full space-time system, multigrid can be used as solver. We analyze this solver with the local Fourier analysis, which gives more insight into the efficiency of the space-time multigrid method. The other option is to decouple the temporal elements and use implicit Runge-Kutta time-stepping methods. We suggest to use Jacobian-free Newton-Krylov (JFNK) solvers since they are advantageous memory-wise. An efficient preconditioner for the Krylov sub-solver is needed to improve the convergence speed. However, we want to avoid constructing or storing the Jacobian, otherwise the favorable memory consumption of the JFNK approach would be obsolete. We present a preconditioner based on an auxiliary first order finite volume replacement operator. Based on the replacement operator we construct an agglomeration multigrid preconditioner with efficient smoothers using pseudo time integrators. Then only the Jacobian of the replacement operator needs to be constructed and the DG method is still Jacobian-free. Numerical experiments for hyperbolic test problems as the advection, advection-diffusion and Euler equations in several dimensions demonstrate the potential of the new approach

Robust stabilised finite element solvers for generalised Newtonian fluid flows

Various materials and solid-fluid mixtures of engineering and biomedical interest can be modelled as generalised Newtonian fluids, as their apparent viscosity depends locally on the flow field. Despite the particular features of such models, it is common practice to combine them with numerical techniques originally conceived for Newtonian fluids, which can bring several issues such as spurious pressure boundary layers, unsuitable natural boundary conditions and coupling terms spoiling the efficiency of nonlinear solvers and preconditioners. In this work, we present a finite element framework dealing with such issues while maintaining low computational cost and simple implementation. The building blocks of our algorithm are (i) an equal-order stabilisation method preserving consistency even for lowest-order discretisations, (ii) robust extrapolation of velocities in the time-dependent case to decouple the rheological law from the overall system, (iii) adaptive time step selection and (iv) a fast physics-based preconditioned Krylov subspace solver, to tackle the relevant range of discretisation parameters including highly varying viscosity. Selected numerical experiments are provided demonstrating the potential of our approach in terms of robustness, accuracy and efficiency for problems of practical interest

Hybridizable compatible finite element discretizations for numerical weather prediction: implementation and analysis

There is a current explosion of interest in new numerical methods for atmospheric modeling. A driving force behind this is the need to be able to simulate, with high efficiency, large-scale geophysical flows on increasingly more parallel computer systems. Many current operational models, including that of the UK Met Office, depend on orthogonal meshes, such as the latitude-longitude grid. This facilitates the development of finite difference discretizations with favorable numerical properties. However, such methods suffer from the ``pole problem," which prohibits the model to make efficient use of a large number of computing processors due to excessive concentration of grid-points at the poles. Recently developed finite element discretizations, known as ``compatible" finite elements, avoid this issue while maintaining the key numerical properties essential for accurate geophysical simulations. Moreover, these properties can be obtained on arbitrary, non-orthogonal meshes. However, the efficient solution of the resulting discrete systems depend on transforming the mixed velocity-pressure (or velocity-pressure-buoyancy) system into an elliptic problem for the pressure. This is not so straightforward within the compatible finite element framework due to inter-element coupling. This thesis supports the proposition that systems arising from compatible finite element discretizations can be solved efficiently using a technique known as ``hybridization." Hybridization removes inter-element coupling while maintaining the desired numerical properties. This permits the construction of sparse, elliptic problems, for which fast solver algorithms are known, using localized algebra. We first introduce the technique for compatible finite element discretizations of simplified atmospheric models. We then develop a general software abstraction for the rapid implementation and composition of hybridization methods, with an emphasis on preconditioning. Finally, we extend the technique for a new compatible method for the full, compressible atmospheric equations used in operational models.Open Acces

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

Smooth and Robust Solutions for Dirichlet Boundary Control of Fluid-Solid Conjugate Heat Transfer Problems

This work offers new computational methods for the optimal control of the conjugate heat transfer (CHT) problem in thermal science. Conjugate heat transfer has many important industrial applications, such as heat exchange processes in power plants and cooling in electronic packaging industry, and has been a staple of computational methods in thermal science for many years. This work considers the Dirichlet boundary control of fluid-solid CHT problems. The CHT system falls into the category of multi-physics problems. Its domain typically consists of two parts, namely, a solid region subject to thermal heating or cooling and a conjugate fluid region responsible for thermal convection transport. These two different physical systems are strongly coupled through the thermal boundary condition at the fluid-solid interface. The objective in the CHT boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the system and a prescribed temperature profile and the cost of the control. This objective is realized by minimizing a nonlinear objective function of the boundary control and the fluid temperature variables, subject to partial differential equations (PDE) constraints governed by the coupled heat diffusion equation in the solid region and mass, momentum and energy conservation equations in the fluid region. Although CHT has received extensive attention as a forward problem, the optimal Dirichlet velocity boundary control for the coupled CHT process to our knowledge is only very sparsely studied analytically or computationally in the literature [131]. Therefore, in Part I, we describe the formulation of the optimal control problem and introduce the building blocks for the finite element modeling of the CHT problem, namely, the diffusion equation for the solid temperature, the convection-diffusion equation for the fluid temperature, the incompressible viscous Navier-Stokes equations for the fluid velocity and pressure, and the model verification of CHT simulations. In Part II, we provide theoretical analysis to explain the nonsmoothness issue which has been observed in this study and in Dirichlet boundary control of Navier-Stokes flows by other scientists. Based on these findings, we use either explicit or implicit numerical smoothing to resolve the nonsmoothness issue. Moreover, we use the numerical continuation on regularization parameters to alleviate the difficulty of locating the global minimum in one shot for highly nonlinear optimization problems even when the initial guess is far from optimal. Two suites of numerical experiments have been provided to demonstrate the feasibility, effectiveness and robustness of the optimization scheme. In Part III, we demonstrate the strategy of achieving parallel scalable algorithms for CHT models in Simulations of Reactor Thermal Hydraulics. Our motivation originates from the observation that parallel processing is necessary for optimal control problems of very large scale, when the simulation of the underlying physics (or PDE constraints) involves millions or billions of degrees of freedom. To achieve the overall scalability of optimal control problems governed by PDE constraints, scalable components that resolve the PDE constraints and their adjoints are the key. In this Part, first we provide the strategy of designing parallel scalable solvers for each building blocks of the CHT modeling, namely, for the discrete diffusive operator, the discrete convection-diffusion operator, and the discrete Navier-Stokes operator. Second, we demonstrate a pair of effective, robust, parallel, and scalable solvers built with collaborators for simulations of reactor thermal hydraulics. Finally, in the the section of future work, we outline the roadmap of parallel and scalable solutions for Dirichlet boundary control of fluid-solid conjugate heat transfer processes

Computational Electromagnetism and Acoustics

It is a moot point to stress the significance of accurate and fast numerical methods for the simulation of electromagnetic fields and sound propagation for modern technology. This has triggered a surge of research in mathematical modeling and numerical analysis aimed to devise and improve methods for computational electromagnetism and acoustics. Numerical techniques for solving the initial boundary value problems underlying both computational electromagnetics and acoustics comprise a wide array of different approaches ranging from integral equation methods to finite differences. Their development faces a few typical challenges: highly oscillatory solutions, control of numerical dispersion, infinite computational domains, ill-conditioned discrete operators, lack of strong ellipticity, hysteresis phenomena, to name only a few. Profound mathematical analysis is indispensable for tackling these issues. Many outstanding contributions at this Oberwolfach conference on Computational Electromagnetism and Acoustics strikingly confirmed the immense recent progress made in the field. To name only a few highlights: there have been breakthroughs in the application and understanding of phase modulation and extraction approaches for the discretization of boundary integral equations at high frequencies. Much has been achieved in the development and analysis of discontinuous Galerkin methods. New insight have been gained into the construction and relationships of absorbing boundary conditions also for periodic media. Considerable progress has been made in the design of stable and space-time adaptive discretization techniques for wave propagation. New ideas have emerged for the fast and robust iterative solution for discrete quasi-static electromagnetic boundary value problems

Direct Numerical Simulation Of Turbulent Flows Using An Implicit Finite Volume Algorithm

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2012Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2012Bu doktora tezi bir Doğrudan Sayısal Benzetim (DNS) uygulama çalışmasını içermektedir. Bu kapsamda, son dönemde önerilen bir çözüm algoritması seçilmiş, bunu temel alan bir paralel DNS çözücüsü geliştirilmiş ve türbülansa geçiş ve hidrodinamik kararsızlık içeren akış problemlerine uygulanmıştır. Bu çalışmanın ana amacı, sıkıştırılamaz ve sıkıştırılabilir türbülanslı akışların DNS metodu ile yapılan modellemesinde araç olarak kullanılabilecek bir çözücü geliştirmek ve bunu araştırmacıların kullanımına sunmak suretiyle bu alana katkıda bulunmaktır. Bir başka amaç da, sözkonusu algoritmayı aynı anda uzaysal ve zamansal olarak çok ölçekli fiziksel mekanizmalar içeren problemlere (örneğin laminer, geçişli ve türbülanslı rejimleri ve değişken Mach sayılarını bir arada içeren hidrodinamik kararsızlıklar) uygulamak yoluyla ileri testlerini yapmak ve üzerinde bazı iyileştirmeler geçekleştirmektir. Bu amaçla, Taylor-Green Vortex (TGV) akışındaki türbülansa geçiş problemi, türbülanslı kayma tabakasındaki (TSL) hıza bağlı karışım problemi ve Rayleigh-Taylor kararsızlığındaki (RTI) yerçekimine bağlı karışım problemi özellikle seçilmiştir. Sıkıştırılabilirlik etkileri de ayrıca incelenmiştir. Sonuçlar, daha önce gerçekleştirilmiş olan teorik, deneysel ve sayısal çalışmaların verileriyle uyum içerisindedir. Sözkonusu karmaşık fiziksel mekanizmalar, seçilen sayısal algoritma ve bunu esas alarak geliştirilen geliştirilen çözücü tarafından doğru bir biçimde elde edilmiştir.This Phd thesis study includes an application of Direct Numerical Simulasyon (DNS). A recently proposed solution algorithm was chosen, a DNS solver based on the algorithm has been developed and applied to the flow problems including transition to turbulence and hydrodynamic instability. The primary objective of this study is to make contributions into this area of modelling incompressible and compressible turbulent flows using DNS by developing an in-house, open source, parallel, implicit solver and presenting it as an open source research tool. Another goal is to perform the assessments of the algorithm and to make some improvements by applying it to the problems including spatial and temporal multi-scale physics simultaneously such as hydrodynamic instabilities where laminar, transitional, and turbulent regimes are found together with varying Mach number regimes. For this purpose, the transition to turbulence problem in Taylor-Green Vortex (TGV), the velocity-induced mixing problem in turbulent shear layer (TSL), and the gravity-induced mixing problem in Rayleigh-Taylor Instability (RTI) were carefully chosen as test cases. The effects of the compressibility were also analyzed. Our results are in agreement with the findings of theoretical results and the previous experimental and numerical studies. The complicated physical mechanisms mentioned above were succesfully captured by the algorithm and the solver as well.DoktoraPh

Robust and stable discrete adjoint solver development for shape optimisation of incompressible flows with industrial applications

PhD, 156ppThis thesis investigates stabilisation of the SIMPLE-family discretisations for incompressible flow and their discrete adjoint counterparts. The SIMPLE method is presented from typical \prediction-correction" point of view, but also using a pressure Schur complement approach, which leads to a wider class of schemes. A novel semicoupled implicit solver with velocity coupling is proposed to improve stability. Skewness correction methods are applied to enhance solver accuracy on non-orthogonal grids. An algebraic multi grid linear solver from the HYPRE library is linked to flow and discrete adjoint solvers to further stabilise the computation and improve the convergence rate. With the improved implementation, both of flow and discrete adjoint solvers can be applied to a wide range of 2D and 3D test cases. Results show that the semi-coupled implicit solver is more robust compared to the standard SIMPLE solver. A shape optimisation of a S-bend air flow duct from a VW Golf vehicle is studied using a CAD-based parametrisation for two Reynolds numbers. The optimised shapes and their flows are analysed to con rm the physical nature of the improvement. A first application of the new stabilised discrete adjoint method to a reverse osmosis (RO) membrane channel flow is presented. A CFD model of the RO membrane process with a membrane boundary condition is added. Two objective functions, pressure drop and permeate flux, are evaluated for various spacer geometries such as open channel, cavity, submerged and zigzag spacer arrangements. The flow and the surface sensitivity of these two objective functions is computed and analysed for these geometries. An optimisation with a node-base parametrisation approach is carried out for the zigzag con guration channel flow in order to reduce the pressure drop. Results indicate that the pressure loss can be reduced by 24% with a slight reduction in permeate flux by 0.43%.Queen Mary-China Scholarship Council Co-funded Scholarship No. 201206280018