Mikael Mortensen

• PhD
• Professor at University of Oslo

Deep reinforcement learning (DRL) has found application in numerous use-cases pertaining to flow control. Multi-agent RL (MARL), a variant of DRL, has shown to be more effective than single-agent RL in controlling flows exhibiting locality and translational invariance. We present, for the first time, an implementation of MARL-based control of three...

This paper describes a fast algorithm for transforming Legendre coefficients into Chebyshev coefficients, and vice versa. The algorithm is based on the fast multipole method and is similar to the approach described by Alpert and Rokhlin [SIAM J. Sci. Comput., 12 (1991)]. The main difference is that we utilise a modal Galerkin approach with Chebyshe...

Deep reinforcement learning (DRL) has found application in numerous use-cases pertaining to flow control. Multi-agent RL (MARL), a variant of DRL, has shown to be more effective than single-agent RL in controlling flows exhibiting locality and translational invariance. We present, for the first time, an implementation of MARL-based control of three...

We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data points (in some cases, our method can learn from a single full-state snapshot), it still achieves high accurac...

This paper presents a new efficient algorithm based on the spectral-Galerkin numerical approximations complemented by a magnetohydrodynamics–Boussinesq model and a new solver for studying the development of a Rayleigh–Taylor (RT) instability. We use the Shenfun computational framework in the Cartesian coordinates, which gives the spectral order and...

Rayleigh–Bénard convection (RBC) is a recurrent phenomenon in a number of industrial and geoscience flows and a well-studied system from a fundamental fluid-mechanics viewpoint. In the present work, we conduct numerical simulations to apply deep reinforcement learning (DRL) for controlling two-dimensional RBC using sensor-based feedback control. We...

Rayleigh-Bénard convection (RBC) is a recurrent phenomenon in a number of industrial and geoscience flows and a well-studied system from a fundamental fluid-mechanics viewpoint. However, controlling RBC, for example by modulating the spatial distribution of the bottom-plate heating in the canonical RBC configuration, remains a challenging topic for...

Two-phase oil and gas flow were simulated in an entirely eccentric annulus and compared with experimental data at horizontal, 4, 10, and 90° inclination. The gas-phase was sulphur hexafluoride and the liquid phase a mixture of Exxsol D60 and Marcol 82 for the inclined cases (5–16), and pure Exxsol D60 for the horizontal cases (1–4). The diameter of...

A novel numerical method has been developed that incorporates electrically conducting objects into particle-in-cell simulations of electrostatic plasma. The method allows multiple objects connected by voltage and current sources in an arbitrary circuit topology. Moreover, by means of an unstructured mesh, the objects can have arbitrary shapes. The...

Co-current two-phase simulations of gas-liquid flow with mixture velocities from 1.2 to 4.2 m/s were run in a partially eccentric annulus and compared with entirely eccentric and concentric experimental data collected at the Institute for Energy Technology in Norway. The gas-phase was sulphur hexafluoride (SF6) for all cases, while the liquid-phase...

Multiphase flow simulations were run in an eccentric annulus. The dimensions of the annulus were 0.1 and 0.05 m for the outer and inner cylinders, respectively, and the mixture velocities were between 1.2 and 4.2 m/s. The simulations were compared with fully eccentric and completely concentric experiments conducted at the Institute for Energy Techn...

Time integration of Fourier pseudo‐spectral DNS is usually performed using the classical fourth‐order accurate Runge–Kutta method, or other methods of second or third order, with a fixed step size. We investigate the use of higher‐order Runge–Kutta pairs and automatic step size control based on local error estimation. We find that the fifth‐order a...

Multiphase flow simulations were run in OpenFOAM utilizing InterFoam, a volume of fluid type solver. A concentric annulus geometry was constructed and periodic boundary conditions were applied to alleviate the requirement for a longer domain. The simulations were run in 3, 5 and 7 m long domains with the annulus dimensioned such that the outer and...

Kinetic simulation results are presented to study the response of multineedle Langmuir probes of the type used on many satellites. Simulations of isolated probes are used to parameterize the current collected as a function of voltage for a set of densities and temperatures relevant to the Earth's ionosphere. These simulations also serve to assess t...

The collected current by spherical and cylindrical Langmuir probes immersed in an unmagnetized and collisionless non-Maxwellian plasma at rest are theoretically studied, and analytical expressions for the currents of attracted and repelled plasma particles are presented. We consider Kappa, Cairns and the generalized Kappa–Cairns distributions as po...

The effect of an external magnetic field on the formation of the wake in the potential distribution behind a dust grain is studied with self-consistent Particle-In-Cell numerical simulations. The collisionless plasma flow is aligned with the magnetic field. It is demonstrated that the topology of the wakefield is significantly affected by the magne...

In free-surface flows, such as breaking ocean waves, the momentum field will have a discontinuity at the interface between the two immiscible fluids, air and water, but still be smooth in most of the domain. Using a higher-order numerical method is more efficient than increasing the number of low-order computational cells in areas where the solutio...

In free-surface flows, such as breaking ocean waves, the momentum field will have a discontinuity at the interface between the two immiscible fluids, air and water, but still be smooth in most of the domain. Using a higher-order numerical method is more efficient than increasing the number of low-order computational cells in areas where the solutio...

We compare three iterative pressure correction schemes for solving the Navier-Stokes equations with a focus on exactly divergence free solution with higher order discontinuous Galerkin discretisations. The investigated schemes are the incremental pressure correction scheme on the standard differential form (IPCS-D), the same scheme on algebraic for...

We present a new method for performing global redistributions of multidimensional arrays essential to parallel fast Fourier (or similar) transforms. Traditional methods use standard all-to-all collective communication of contiguous memory buffers, thus necessarily requiring local data realignment steps intermixed in-between redistribution and trans...

Time integration of Fourier pseudo-spectral DNS is usually performed using the classical fourth-order accurate Runge--Kutta method, or other methods of second or third order, with a fixed step size. We investigate the use of higher-order Runge-Kutta pairs and automatic step size control based on local error estimation. We find that the fifth-order...

Multiscale or multiphysics problems often involve coupling of partial differential equations posed on domains of different dimensionality. In this work, we consider a simplified model problem of a 3d‐1d coupling and the main objective is to construct algorithms that may utilize standard multilevel algorithms for the 3d domain, which has the dominat...

The utility of flow simulations relies on the robustness of computational fluid dynamics (CFD) solvers and reproducibility of results. The aim of this study was to validate the Oasis CFD solver against in vitro experimental measurements of jet breakdown location from the FDA nozzle benchmark at Reynolds number 3500, which is in the particularly cha...

The potential and density wake behind a finite-sized object in a magnetized collisionless plasma flow is studied with self-consistent numerical simulations. With increasing magnetization of the plasma, the standard picture of ion focusing in the wake for plasmas with large electron to ion temperature ratios becomes invalid. A strong magnetic field...

We present a new method for performing global redistributions of multidimensional arrays essential to parallel fast Fourier (or similar) transforms. Traditional methods use standard all-to-all collective communication of contiguous memory buffers, thus necessary requiring local data realignment steps intermixed in-between redistribution and transfo...

Solving the Navier-Stokes equations when the density field contains a large sharp discontinuity---such as a water/air free surface---is numerically challenging. Convective instabilities cause Gibbs oscillations which quickly destroy the solution. We investigate the use of slope limiters for the velocity field to overcome this problem in a way that...

Solving the Navier-Stokes equations when the density field contains a large sharp discontinuity---such as a water/air free surface---is numerically challenging. Convective instabilities cause Gibbs oscillations which quickly destroy the solution. We investigate the use of slope limiters for the velocity field to overcome this problem in a way that...

The electric potential distribution around a dust particle immersed in a magnetised supersonic plasma flow is studied by numerical simulations. It is shown that with increasing magnetisation of plasma, the peak in the wake potential gets smaller and moves upstream. For strong magnetisation, the trailing peak in the potential distribution vanishes a...

The charging of a sounding rocket in subsonic and supersonic plasma flows with external magnetic field is studied with numerical particle-in-cell (PIC) simulations. A weakly magnetized plasma regime is considered that corresponds to the ionospheric F2 layer, with electrons being strongly magnetized, while the magnetization of ions is weak. It is de...

Direct numerical simulation of the interlayer region above bio-inspired micro-surfaces using FEniCS and OASIS

With the shenfun Python module (github.com/spectralDNS/shenfun) an effort is made towards automating the implementation of the spectral Galerkin method for simple tensor product domains, consisting of (currently) one non-periodic and any number of periodic directions. The user interface to shenfun is intentionally made very similar to FEniCS (fenic...

Intrathecal drug and gene vector delivery is a procedure to release a solute within the cerebrospinal fluid. This procedure is currently used in clinical practice and shows promise for treatment of several central nervous system pathologies. However, intrathecal delivery protocols and systems are not yet optimized. The aim of this study was to inve...

A fully (pseudo-)spectral solver for direct numerical simulations of large-scale turbulent channel flows is described. The solver utilizes the Chebyshev base functions suggested by J. Shen [SIAM J. Sci. Comput., 16, 1, 1995], that lead to stable and robust numerical schemes, even at very large scale. New and fast algorithms for the direct solution...

Multiscale or multiphysics problems often involve the coupling of partial differential equations posed on domains of different dimensionality. In this work we consider a simplified model problem of a 3$d$-1$d$ coupling and the main motivation is to construct algorithms that may utilize standard multilevel algorithms for the 3$d$ domain, which has t...

The Neumann problem of linear elasticity is singular with a kernel formed by the rigid motions of the body. There are several tricks that are commonly used to obtain a non-singular linear system. However, they often cause reduced accuracy or lead to poor convergence of the iterative solvers. In this paper, four different well-posed formulations of...

The Neumann problem of linear elasticity is singular with a kernel formed by the rigid motions of the body. There are several tricks that are commonly used to obtain a non-singular linear system. However, they often cause reduced accuracy or lead to poor convergence of the iterative solvers. In this paper, different well-posed formulations of the p...

Direct Numerical Simulations (DNS) of the Navier Stokes equations is a valuable research tool in fluid dynamics, but there are very few publicly available codes and, due to heavy number crunching, codes are usually written in low-level languages. In this work a \textasciitilde{}100 line standard scientific Python DNS code is described that nearly m...

We study preconditioners for a model problem describing the coupling of two elliptic subproblems posed over domains with different topological dimension by a parameter dependent constraint. A pair of parameter robust and efficient preconditioners is proposed and analyzed. Robustness and efficiency of the preconditioners is demonstrated by numerical...

We study preconditioners for a model problem describing the coupling of two elliptic subproblems posed over domains with different topological dimension by a parameter dependent constraint. A pair of parameter robust and efficient preconditioners is proposed and analyzed. Robustness and efficiency of the preconditioners is demonstrated by numerical...

Oasis is a high-level/high-performance finite element Navier-Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the l...

Direct Numerical Simulations (DNS) of the Navier Stokes equations is an invaluable research tool in fluid dynamics. Still, there are few publicly available research codes and, due to the heavy number crunching implied, available codes are usually written in low-level languages such as C/C++ or Fortran. In this paper we describe a pure scientific Py...

Direct Numerical Simulations (DNS) of the Navier Stokes equations is an invaluable research tool in fluid dynamics. Still, there are few publicly available research codes and, due to the heavy number crunching implied, available codes are usually written in low-level languages such as C/C++ or Fortran. In this paper we describe a pure scientific Py...

We present an overview of the continuous and discontinuous Galerkin finite element methods (CG-FEM, DG-FEM) for numerical solution of the transport equation and show how the Navier-Stokes equations can be solved with CG-FEM in both a coupled and segregated manner. We show convergence of the implemented Navier-Stokes solvers for single-phase flows o...

We present a lightweight Python module for computing small deformations of a single plate supported by an arbitrary number of possibly intersecting stiffeners. We show how the problem fits into the framework of abstract saddle point problems and how this abstraction can be exploited for clean design of the code. Stability properties of the resultin...

The Neumann problem for linear elasticity is singular with a kernel formed by rigid motions. Unless removed, the kernel causes problems for both direct and iterative methods. In this paper we shall first discuss how the basis of the nullspace may be used to formulate a well posed problem. Afterwards we present a simple and efficient technique for c...

Oasis is an open-source Computational Fluid Dynamics solver designed to handle both laminar, transitional, and fully developed turbulent flows. Oasis has been developed by combining FEniCS' (http://fenicsproject.org/) user-friendly Python interface with highly optimized energy conserving numerical schemes, where the incompress-ible Navier-Stokes eq...

Numerical simulations of hydrodynamics (HD) and magneto-hydrodynamics (MHD) Kelvin-Helmholtz (KH) instability are performed by means of a pseudo-spectral (PS) Fourier-Galerkin method. The PS method is used to solve the Navier-Stokes and MHD equations with Boussinesq approximation numerically. The code is parallel and it is written entirely in Pytho...

Oasis is a high-level/high-performance finite element Navier–Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the l...

This paper assesses the Presumed Mapping Function (PMF) approach in the context of the Stationary Laminar Flamelet Modelling (SLFM) of a reacting Double Scalar Mixing Layer (DSML). Starting from a prescribed Gaussian reference field, the PMF approach provides a presumed Probability Density Function (PDF) for the mixture fraction that is subsequentl...

Numerical algorithms for the computation of fluid flow have been an active area of research for 12062 several decades and still remain an important field to study. As a result, there exists a large literature 12063 on discretization schemes for the incompressible Navier–Stokes equations, and it can be hard to 12064 judge which method works best for...

Computational fluid dynamics, CFD, has become an indispensable tool for many engineers. This book gives an introduction to CFD simulations of turbulence, mixing, reaction, combustion and multiphase flows. The emphasis on understanding the physics of these flows helps the engineer to select appropriate models to obtain reliable simulations. Besides...

The purpose of this work is to validate Navier–Stokes (NS) solvers implemented in FEniCS for 12416 unstable, transitional flows. Solvers for the NS equations have been discussed in Chapter 21 for 12417 laminar flows. In this chapter, focus is put more directly on energy and energy conservation, features 12418 of primary importance in turbulence app...

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynold...

In this work the original V2F model of Durbin (Theor. Comput. Fluid Dyn. 3:1–13, 1991) and the nonlinear V2F model of Pettersson Reif (Flow Turbul. Combust. 76:241–256, 2006) have been assessed for several adverse pressure gradient (APG) turbulent boundary layer flows, designed as benchmark cases within the WALLTURB consortium. The APG flows have b...

In this paper a one-way coupling between the nonlinear v In this paper a one-way coupling between the nonlinear v 2 − f model by Pettersson Reif (Flow Turbul Combust 76:241–256, 2006) and an algebraic structure-based model have been investigated. Comparisons with available experimental and numerical data 2 − f model by Pettersson Reif (Flow Turbul...

The objective of this paper is to assess the accuracy of low-order finite volume (FV) methods applied to the v2 − f turbulence model of Durbin (Theoret. Comput. Fluid Dyn. 1991; 3:1–13) in the near vicinity of solid walls. We are not (like many others) concerned with the stability of solvers - the topic at hand is simply whether the mathematical pr...

In this work we derive the fundamental equations for conditional moment closure (CMC) modelling of individual phases set in a two-phase flow. The derivation is based on the instantaneous transport equations for the single phase that involve a level set/indicator function technique for accounting for interfaces. Special emphasis is put on spray comb...

In this work we derive the fundamental equations for conditional moment closure (CMC) modelling of individual phases set in a two-phase flow. The derivation is based on the instantaneous transport equations for the single phase that involve a level set/indicator function technique for accounting for interfaces. Special emphasis is put on spray comb...

In this work we use 3D direct numerical simulations (DNS) to investigate the average velocity conditioned on a conserved scalar in a double scalar mixing layer (DSML). The DSML is a canonical multistream flow designed as a model problem for the extensively studied piloted diffusion flames. The conditional mean velocity appears as an unclosed term i...

The reacting double scalar mixing layer (RDSML) is investigated as a canonical multistream flow and a model problem for simple piloted diffusion flames. In piloted diffusion flames, the reacting fuel and oxidizer streams are initially separated by a central pilot stream at stoichiometric composition. The primary purpose of this pilot is to delay th...

The double scalar mixing layer (DSML) is a canonical problem for studying the mixing of multiple streams and, with reaction, combustion of the partially premixed type. In a DSML, a third stream consisting of a premixture of the reactants is introduced in between the pure fuel and air streams of the classic twin-feed or binary mixing problem. The we...

The mapping closure of Chen et al. [Phys. Rev. Lett., 63, 1989] is a transported probability density function (PDF) method that has proven very efficient for modelling of turbulent mixing in homogeneous turbulence. By utilizing a Gaussian reference field, the solution to the mapping function (in homogeneous turbulence) can be found analytically for...

Conditional scalar mixing statistics from a three-dimensional direct numerical simulation (DNS) of a scalar mixing layer are presented in the context of modeling non-premixed turbulent combustion. The simulation is closely matched to a particular laboratory experiment but with slight adjustments so that the simulated flow is very nearly self-simila...

In this Brief Communication we describe a consistent method for calculating the conditional scalar dissipation (or diffusion) rate for inhomogeneous turbulent flows. The model follows from the transport equation for the conserved scalar probability density function (PDF) using a gradient diffusion closure for the conditional mean velocity and a pre...

Mathematical models of non-premixed turbulent reacting flows were developed. The models were used both by the chemical process industry and turbulent combustion applications. A model was also developed for the rate of molecular mixing of a conserved scalar. A new approach for modeling of presumed probability distribution functions (PDF), based on t...

An implementation of the conditional moment closure (CMC) of Bilger (Phy. Fluids A 5 (1993) 436) and Klimenko (Fluid Dyn. 25 (1990) 327) has been carried out in the commercial CFD software FLUENT. A new implementation method is suggested that uses the CMC-equations to calculate an unconditional reaction rate that is subsequently inserted in a Reyno...

Planar laser induced fluorescence measurements were performed on a passive tracer coaxially injected in the center of a larger pipe carrying intermediate to fully turbulent flows. Axial distributions of mean concentration and concentration variance for the tracer are presented. Results were compared with theoretical predictions of two multiple-time...

Mixing of two liquids in a new multifunctional channel reactor developed by AlfaLaval has been studied both experimentally and through computational fluid dynamics (CFD). As the channels are quite narrow the Reynolds numbers are low and the bulk of the channel is within the turbulent boundary layer. This makes accurate a priori predictions of the f...

Mixing of two liquids in a new multifunctional channel reactor developed by AlfaLaval has been studied both experimentally and through computational fluid dynamics (CFD). As the channels are quite narrow the Reynolds numbers are low and the bulk of the channel is within the turbulent boundary layer. This makes accurate a priori predictions of the f...

Planar laser induced fluorescence measurements were performed on a passive tracer coaxially injected in the center of a larger pipe carrying intermediate to fully turbulent flows. Axial distributions of mean concentration and concentration variance for the tracer are presented. Results were compared with theoretical predictions of two multiple-time...