Research interests

Continuous Galerkin Methods: one of my research interests are high-resolution finite element methods based on a novel class of genuinely multi-dimensional algebraic flux correction (AFC) techniques. I developed an edge-based solver for steady state and time-dependent compressible flows on fully unstructured meshes and combined it with dynamical mesh adaptation techniques based on gradient recovery-based error indicators and a posteriori goal-oriented error estimation techniques.

Isogeometric Analysis: I am also working in the field of isogeometric Galerkin methods for flow problems with special emphasis on order-adaptive high-resolution techniques and their efficient implementation on many-core hardware such as GPGPUs or the Intel Many-Integrated Core Architecture.

Fast Solvers: I am, moreover, interested in computationally efficient solution methods with special emphasis on nonlinear Newton-type solvers with approximate Jacobians, geometric multi-grid solvers for flow problems and positivity-preserving implicit time-stepping schemes.

HPC: another field of interest are parallel computing techniques for many- and multi-core systems with special emphasis on the efficient assembly of finite element forms.

Software: most of my research on finite elements for flow problems is pursued in the open-source software package Featflow2. My research in the field of isogeometric analysis is pursued in the open-source C++ library G+Smo. I am moreover main developed of the Fluid Dynamic Building Block library.

PhD projects

If you are interested in pursuing your PhD studies under my supervision please contact me for an appointment.

High-order material point method

Roel Tielen, TU Delft (daily supervisor)

Adjoint-based optimization in turbomachinery applications

Andrzej Jaeschke, TU Lodz (remotr supervisor)

Design optimization of rotary screw machines

Jochen Hinz, TU Delft (PI and daily supervisor)

This PhD-project is part of the H2020 project Multi-ObjecTive design Optimization of fluid eneRgy machines (MOTOR, GA No. 672787)

General description

Fluid energy machines such as aircraft engines, ship propellers, water turbines, and rotary twin screw machines have a broad field of applications in transportation systems, for electricity generation and in industrial applications as compressors and expanders. The MOTOR project focuses on the design optimization of fluid energy machines with respect to multiple target quantities such as high efficiency over a broad range of operational conditions and enhanced resilience. At the same time, the aim is to reduce the time of the design process significantly by using advanced numerical modeling and simulation techniques and automated design optimization tools.

The common principle of fluid energy machines is to transfer mechanical energy to and from the surrounding fluid. The performance of these machines essentially depends on the shape of their geometry, which is described by functional free-form surfaces. The challenge in their design is that even small modifications of tiny details can have significant impact on the overall performance. It is therefore necessary to have (a) a very accurate representation of the geometry, (b) to use very accurate simulation and optimization tools, and (c) to reduce or, at best, completely eliminate approximate conversion steps that introduce additional errors.

The vision of the MOTOR project is to link all computational tools involved in the design, simulation and optimization of fluid energy machines to the same representation of the geometry, thereby reducing the number of approximate conversion steps and enabling a fully automated simulation-driven design optimization.

Project objectives

The project aims at developing a simulation and optimization toolbox for the CFD analysis of rotary twin screw machines and the simulation-driven optimization of the rotor profiles. The working principle of these machines is remarkably simple. Two counter-rotating helical screw, known as male and female rotors, force the fluid (air or other gases) from the suction side to the outlet, thereby either compressing or expanding it. The effectiveness of this mechanism depends on many factors, in particular, on the rotor pitch. The rotors of commercial screw compressors and expanders are mostly build with constant pitch but examples of variable pitch rotors indicate enhanced efficiencies.

PhD project

The goal of this PhD project is to develop a computational tool to generate analysis-suitable multi-variate parameterizations of screw machine geometries. Together with the Chair of Fluidics at TU Dortmund University, which is one of the world’s leading experts in this field, adaptive spline parameterization techniques are developed to enable the accurate parameterization of the male and female rotor and the casing in 2D (slices) and 3D, respectively. The major challenge is is the accurate representation of the clearances (0.4mm) between the two rotors and a single rotor and the casing.

Non-physical oscillations in the simulation of foam enhanced oil recovery

Jakolien van der Meer, TU Delft (co-promoter)

If secondary hydrocarbon recovery methods, like gas flooding, fail because of the occurrence of gravity override and viscous fingering one can turn to an enhanced oil recovery method (EOR) like the injection of foam. The generation of foam can be described by a set of partial differential equations with strongly nonlinear functions, which impose challenges for the numerical modeling. Former studies by [Zanganeh 2011] and [Ashoori 2012] show the occurrence of strongly temporally oscillating solutions when using forward simulation models, that are entirely due to discretization artifacts.

To analyze these problems, we study the dynamics of a simplified foam model based on the Buckley-Leverett equation. Whereas the Buckley-Leverett flux is a smooth function of water saturation, the foam will cause a rapid increase of the flux function over a very small saturation scale. Consequently the derivatives of the flux function can become extremely large and impose a severe constraint on the time step due to the CFL condition.

We make use of two different approaches to tackle these problems. The first approach is a variant of the standard finite volume discretization, where we make use of analytical techniques to take into account the strong nonlinearity in the coefficients. The second approach involves the use of adaptive flux correction transport (AFCT) methods, where we mollify the influence of the anti-diffusive terms that may destroy positivity [Kuzmin 2012]. These methods are applied to the simplified foam model in one dimension, and will be extended to two dimensions and to a more complex foam model.

The goal of this research is to come up with easy applicable techniques to solve the problem of the time oscillations. These can be used in commercial simulators (MoReS (Shell)), to optimize the amount of surfactant needed to give a profitable output.

Literature

  • E. Ashoori. Foam for Enhanced Oil Recovery: Modeling and Analytical Solutions. PhD thesis, Delft University of Technology, 2012.
  • D. Kuzmin. Linearity-preserving flux correction and convergence acceleration for constrained Galerkin schemes. Journal of Computational and Applied Mathematics, 236(9): 2317–2337, 2012.
  • M. Namdar Zanganeh. Simulation and optimization of foam EOR processes. PhD thesis, Delft University of Technology, 2011.

Isogeometric analysis of two-phase flows with the Cahn-Hilliard phase field model

Babak S. Hosseini, TU Dortmund (remote supervisor)

MSc projects

If you are interested in doing your masters project under my supervision check the available topics. If you have an idea for another topic that you would like to work on please contact me for an appointment.

  • AVAILABLE: Isogeometric Analysis in Industrial Turbomachinery Applications (project description)
  • AVAILABLE: Energy-efficient multigrid solution strategies and their application in dataflow computing (project description)
  • Efficient solution of Poisson's equation by the variational collocation method using dataflow computing (Marlijn van Veen, start February 2017, project description, link)
  • Towards a Material Point Method with Powell-Sabin spline basis functions: MPM with higher-order C1-continuous basis functions on triangulations (Pascal de Koster, supervisor together with Vahid Galavi from Deltares, Thesis finished August 2018, project description)
  • Solving Poisson's equation using dataflow computing (Ruben van Nieuwpoort, supervisor together with Georgi Gaydadjiev, Thesis finished December 2017, project description, link)
  • High performance data traversal: Cache aware computing with space filling curve (Sagar Dolas, supervisor together with Vahid Galavi from Deltares, Thesis finished August 2017, project description, link)
  • Multi-patch discontinuous Galerkin isogeometric analysis for porous media flow (Kenny David, supervisor, Thesis finished January 2017 , project description, link)
  • High-order material point method (Roel Tielen, supervisor together with Lars Beuth from Deltares, Thesis finished July 2016, project description, link)
  • Compatible isogeometric discretizations for the incompressible Euler equations (Stevie-Ray Janssen, supervisor together with Mark Gerritsma from Aerospace Engineering TU Delft, Thesis finished November 2016, link)
  • Isogeometric analysis for a reaction-diffusion model of human brain development (Jochen Hinz, supervisor together with Fred Vermolen, Thesis finished January 2016, link)
  • Towards a multiscale discrete particle model for stability prediction of granular flood defences (Jakob Maljaars, co-supervisor, Thesis finished January 2016)
  • Application of the algebraic flux correction algorithm to a one-dimensional water flood model (Prakhar Agarwal, co-supervisor, start November 2014, project description, link)
  • Isogeometric analysis for compressible flows with application in turbomachinery (Andrzej Jaeschke, supervisor, Thesis finished August 2015, project description, link)
  • Numerical methods for differential algebraic equations (Kristin Altmann, co-supervisor, Thesis finished February 2015, project description, link)
  • Untersuchungen einer Brinkmann-Penalty-Methode kombiniert mit hochauflösendem FEM-FCT zur Approximativen Lösung der kompressiblen Euler-Gleichungen (Malte Schuh, supervisor, finished December 2015, TU Dortmund)

BSc projects

If you are interested in doing your bachelor project under my supervision check the available topics. If you have an idea for another topic that you would like to work on please contact me for an appointment.

  • Beyond IEEE-754 floating point arithmetic: UNUM 2.0 (Stan van der Linde, started February 2018)
  • Quantum-accelerated numerical linear algebra (Rutger Nugteren, started February 2018)
  • Implementation and Analysis of an Algorithm on Positive Integer Addition for Quantum Computing (Menno Looman, Thesis, finished August 2018 at TU Delft)
  • Quantum algorithms and their implementation on quantum computer simulators (Mike van der Lans, supervisor together with Carmina Almudever from QuTech, Thesis finished June 2018 at TU Delft)
  • The effect of rational heat transfer on the behavior of surge vessels (Merel Toussaint, co-supervisor, Thesis finished January 2015 at TU Delft)
  • Mathematische Modellierung und Untersuchung des Bewegungsverhaltens eines Stehaufkreisels (Sophia Bremm, supervisor, finished April 2014 at TU Dortmund)
  • Numerische Verfahren für die kompressiblen Eulergleichungen mit Anwendung (Christoph Lohmann, supervisor, Thesis finished January 2014 at TU Dortmund)
  • Line Integral Convolution - Texturbasierte Strömungsvisualisierung (Florian Imorde, supervisor, finished December 2013 at TU Dortmund)
  • Numerische Behandlung der Konvektions-Diffusionsgleichung mittels ALE Finite Elemente Methode (Jens Köhler, supervisor, finished November 2013 at TU Dortmund)
  • Numerischer Vergleich nichtlinearer und linearer Mehrgitterverfahren zum Lösen von partiellen Differentialgleichungen (Mirco Altenbernd, supervisor, Thesis finished September 2013 at TU Dortmund)
  • PDE-basierte Bildverbesserungsalgorithmen: Konstruktion und numerischer Vergleich verschiedener Diffusionsoperatoren (Malte Schirwon, supervisor, finished September 2013 at TU Dortmund)
  • Numerische Analyse von Runge-Kutta Verfahren im Kontext von FEM Ortsdiskretisierungen am Beispiel der Konvektions-Diffusions-Gleichung (Ramona Sasse, supervisor, Thesis finished Juli 2013 at TU Dortmund)
  • Einfluss verschiedener Färbungsstrategien auf parallele numerische Algorithmen (Matthias Cebulla, co-supervisor, Thesis finished December 2012 at TU Dortmund)

Honours Programme Delft

If you are interested in doing the Honours Programme Delft under my supervision please write me an e-mail to discuss possible topics.

  • Smart software technologies for enabling next-generation hardware-oriented scientific computing (Dennis Pouw, started October 2016):

    Scientific Computing is a rapidly growing multidisciplinary field that makes use of advanced technologies from computer science, electrical engineering and applied mathematics to solve real-world problems. For instance, the design of next-generation environmental friendly aircrafts that require less fuel and emit less noise is a multi- disciplinary, multi-objective optimization problem. It involves the solution of huge linear and nonlinear problems with millions and even billions of unknown quantities that call for the use of large parallel computers, so-called High-Performance Computers (HPC).

    A recent trend in HPC is the use of reconfigurable hardware (e.g., Field Programmable Gate Arrays) either as stand-alone device or in the form of hybrid CPU-FPGAs. The dream is to bring utmost flexibility to the user by allowing him or her to create the optimal hardware design for a particular algorithm without hardly any constraints observed in commodity hardware. However, with s technologies it is still a challenge to program these devices in a user-friendly way.

    In previous collaborations, the Numerical Analysis group worked together with Maxeler Technologies, who is at the forefront of establishing reconfigurable hardware in HPC. s MaxJ programming language is an extension of Java that makes it possible to implement algorithms on FPGAs. Nonetheless, developing algorithms for FPGAs is still far more rudimentary than writing elegant code using smart programming techniques.

    The aim of this project is to develop a smart expression template library for FPGAs that allows to write algorithms in high-level notation, which is automagically transformed into s MaxJ programming language and, in turn, compiled into FPGA hardware code. As a starting point, the VexCL library, which realizes the sketched approach for the OpenCL and s CUDA programming language, shall be extended towards MaxJ. In a second step, optimized compute kernels for FPGAs shall be integrated. The final aim of this project is to develop a proof-of-concept application that demonstrates the potential of this smart expression template library for programming FPGAs.

  • Modelling of traffic flow using macroscopic approaches (Hans de Munnik, started September 2015):

    The number of cars (and bicycles) increases from year to year causing traffic jams and accidents. Since decades, mathematicians work on models that are able to predict traffic flow and help to optimise the duration of traffic light cycles, speed limits, position of driveways, etc. The widely accepted Lighthill-Whitham-Richards macroscopic model is based on the observation that the number of cars on a one-lane road without driveways is conserved over time. This leads to so-called conservation laws (partial differential equations) which are also known from physical principles (conservation of mass, momentum, and energy). For simple set-ups, the traffic flow model admits an analytic solution but, in general, numerical methods are required. The goal of this project is to implement a traffic flow simulator for predicting the flow of cars (or bicycles) on the roads, to study the influence of selected controlling factors and to optimise, e.g., the duration of traffic light cycles for a particular scenario.