# Benjamin SanderseCentrum Wiskunde & Informatica | CWI · Research Group for Scientific Computing

Benjamin Sanderse

PhD, MSc

## About

57

Publications

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939

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Introduction

Additional affiliations

October 2008 - December 2012

October 2008 - December 2012

October 2008 - December 2012

## Publications

Publications (57)

Wind farm flow control aims to improve wind turbine performance by reducing aerodynamic wake interaction between turbines. Dynamic, physics-based models of wind farm flows have been essential for exploring control strategies such as wake redirection and dynamic induction control. Free vortex methods can provide a computationally efficient way to mo...

Simulating multi-scale phenomena such as turbulent fluid flows is typically computationally very expensive. Filtering the smaller scales allows for using coarse discretizations, however, this requires closure models to account for the effects of the unresolved on the resolved scales. The common approach is to filter the continuous equations, but th...

Projection-based model order reduction of an ordinary differential equation (ODE) results in a projected ODE. Based on this ODE, an existing reduced-order model (ROM) for finite volume discretizations satisfies the underlying conservation law over arbitrarily chosen subdomains. However, this ROM does not satisfy the projected ODE exactly but introd...

FLORIDyn is a parametric control-oriented dynamic model suitable to predict the dynamic wake interactions between wind turbines in a wind farm. In order to improve the accuracy of FLORIDyn, this study proposes to calibrate the tuning parameters present in the model by employing a probabilistic setting using the UQ4WIND framework. The strategy relie...

We show that the one-dimensional (1D) two-fluid model (TFM) for stratified flow in channels and pipes (in its incompressible, isothermal form) satisfies an energy conservation equation, which arises naturally from the mass and momentum conservation equations that constitute the model. This result extends upon earlier work on the shallow water equat...

Control-oriented models provide a basis for wind farm control to improve power production and reduce structural loading. Wake steering is considered to be one of the most promising techniques to achieve this. Wind turbine wakes under yaw misalignment are deflected downstream and have been shown to produce a curled or kidney-shaped structure. A Navi...

This paper presents an efficient strategy for the Bayesian calibration of parameters of aerodynamic wind turbine models. The strategy relies on constructing a surrogate model (based on adaptive polynomial chaos expansions), which is used to perform both parameter selection using global sensitivity analysis and parameter calibration with Bayesian in...

In the context of solving inverse problems for physics applications within a Bayesian framework, we present a new approach, Markov Chain Generative Adversarial Neural Networks (MCGANs), to alleviate the computational costs associated with solving the Bayesian inference problem. GANs pose a very suitable framework to aid in the solution of Bayesian...

Many countries are currently dealing with the COVID-19 epidemic and are searching for an exit strategy such that life in society can return to normal. To support this search, computational models are used to predict the spread of the virus and to assess the efficacy of policy measures before actual implementation. The model output has to be interpr...

This paper presents an efficient strategy for the Bayesian calibration of parameters of aerodynamic wind turbine models. The strategy relies on constructing a surrogate model (based on adaptive polynomial chaos expansions), which is used to perform both parameter selection using global sensitivity analysis and parameter calibration with Bayesian in...

Traditional fluid flow predictions require large computational resources. Despite recent progress in parallel and GPU computing, the ability to run fluid flow predictions in real-time is often infeasible. Recently developed machine learning approaches, which are trained on high-fidelity data, perform unsatisfactorily outside the training set and re...

A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This ‘discretize‐then‐project’ approach requires no pressure stabilization technique (even though the pressure term is present in the ROM) nor a boundary control t...

The one-dimensional (1D) two-fluid model (TFM) for stratified flow in channels and pipes suffers from an ill-posedness issue: it is only conditionally well-posed. This results in severe linear instability for perturbations of vanishing wavelength, and non-convergence of numerical solutions. This issue is typically only examined from the perspective...

Many countries are currently dealing with the COVID-19 epidemic and are searching for an exit strategy such that life in society can return to normal. To support this search, computational models are used to predict the spread of the virus and to assess the efficacy of policy measures before actual implementation. The model output has to be interpr...

A novel mathematical framework is derived for the addition of nodes to univariate and interpolatory quadrature rules. The framework is based on the geometrical interpretation of the Vandermonde matrix describing the relation between the nodes and the weights and can be used to determine all nodes that can be added to an interpolatory quadrature rul...

A novel pressure-free two-fluid model formulation is proposed for the simulation of one-dimensional incompressible multiphase flow in pipelines and channels. The model is obtained by simultaneously eliminating the volume constraint and the pressure from the widely used two-fluid model (TFM). The resulting ‘pressure-free two-fluid model’ (PF-TFM) ha...

A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This 'discretize-then-project' approach requires no pressure stabilization technique (even though the pressure term is present in the ROM) nor a boundary control t...

A framework is presented for performing global sensitivity analysis of model parameters associated with the Blade Element Momentum (BEM) models. Sobol indices based on adaptive sparse polynomial expansions are used as a measure of global sensitivities. The sensitivity analysis workflow is developed using the uncertainty quantification toolbox UQLab...

The general goal of the work reported in this paper is to gain more confidence when performing blade element momentum (BEM)-based aeroelastic simulations, especially when setting-up sub-models and their parameters. Due to limited or no information, the set-up of these methods is often highly uncertain. To achieve this objective, we have developed a...

A novel reduced-order model (ROM) formulation for incompressible flows is presented with the key property that it exhibits non-linearly stability, independent of the mesh (of the full order model), the time step, the viscosity, and the number of modes. The two essential elements to non-linear stability are: (1) first discretise the full order model...

A novel approach is proposed to reduce, compared with the conventional binning approach, the large number of aeroelastic code evaluations that are necessary to obtain equivalent loads acting on wind turbines. These loads describe the effect of long‐term environmental variability on the fatigue loads of a horizontal‐axis wind turbine. In particular,...

A novel method is proposed to infer Bayesian predictions of computationally expensive models. The method is based on the construction of quadrature rules, which are well-suited for approximating the weighted integrals occurring in Bayesian prediction. The novel idea is to construct a sequence of nested quadrature rules with positive weights that co...

A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good approximation independent of the actual grid level. Our method learns this structure by employing a sequence of conv...

A novel pressure-free two-fluid model formulation is proposed for the simulation of one-dimensional incompressible multiphase flow in pipelines and channels. The model is obtained by simultaneously eliminating the volume constraint and the pressure from the widely used two-fluid model (TFM). The resulting `pressure-free two-fluid model' (PF-TFM) ha...

A novel reduced order model (ROM) formulation for incompressible flows is presented with the key property that it possesses non-linear stability, independent of the mesh (of the full order model), the time step, the viscosity, and the number of modes. The two essential elements to non-linear stability are: (1) first discretise the full order model,...

A novel method is proposed to infer Bayesian predictions of computationally expensive models. The method is based on the construction of quadrature rules, which are well-suited for approximating the weighted integrals occurring in Bayesian prediction. The novel idea is to construct a sequence of nested quadrature rules with positive weights that co...

A novel refinement measure for non-intrusive surrogate modelling of partial differential equations (PDEs) with uncertain parameters is proposed. Our approach uses an empirical interpolation procedure, where the proposed refinement measure is based on a PDE residual and probability density function of the uncertain parameters, and excludes parts of...

Multiphase flows are described by the multiphase Navier-Stokes equations. Numerically solving these equations is computationally expensive, and performing many simulations for the purpose of design, optimization and uncertainty quantification is often prohibitively expensive. A simplified model, the so-called two-fluid model, can be derived from a...

A novel approach is proposed to reduce, compared to the conventional binning approach, the large number of aeroelastic code evaluations that are necessary to obtain equivalent loads acting on wind turbines. These loads describe the effect of long-term environmental variability on the fatigue loads of a horizontal-axis wind turbine. In particular De...

A novel mathematical framework is derived for the addition of nodes to interpolatory quadrature rules. The framework is based on the geometrical interpretation of the Vandermonde-matrix describing the relation between the nodes and the weights and can be used to determine all nodes that can be added to an interpolatory quadrature rule with positive...

New time integration methods are proposed for simulating incompressible multiphase flow in pipelines described by the one-dimensional two-fluid model. The methodology is based on ‘half-explicit’ Runge–Kutta methods, being explicit for the mass and momentum equations and implicit for the volume constraint. These half-explicit methods are constraint-...

For the purpose of uncertainty propagation a new quadrature rule technique is proposed that has positive weights, has high degree, and is constructed using only samples that describe the probability distribution of the uncertain parameters. Moreover, nodes can be added to the quadrature rule, resulting into a sequence of nested rules. The rule is c...

New time integration methods are proposed for simulating incompressible multiphase flow in pipelines described by the one-dimensional two-fluid model. The methodology is based on 'half-explicit' Runge-Kutta methods, being explicit for the mass and momentum equations and implicit for the volume constraint. These half-explicit methods are constraint-...

During the design phase of an offshore wind turbine, it is required to assess the impact of loads on the turbine life time. Due to the varying environmental conditions, the effect of various uncertain parameters has to be studied to provide meaningful conclusions. Incorporating such uncertain parameters in this regard is often done by applying binn...

A novel approach for non-intrusive uncertainty propagation is proposed. Our approach overcomes the limitation of many traditional methods, such as generalised polynomial chaos methods, which may lack sufficient accuracy when the quantity of interest depends discontinuously on the input parameters. As a remedy we propose an adaptive sampling algorit...

An efficient algorithm is proposed for Bayesian model calibration, which is commonly used to estimate the model parameters of non-linear, computationally expensive models using measurement data. The approach is based on Bayesian statistics: using a prior distribution and a likelihood, the posterior distribution is obtained through application of Ba...

Uncertainties are omnipresent in wind energy applications, both in external conditions (such as wind and waves) as well as in the models that are used to predict key quantities such as costs, energy yield, and fatigue loads. This report summarizes and reviews the application of uncertainty quantification techniques to wind energy problems. In the w...

One-dimensional models for multiphase flow in pipelines are commonly discretised using first-order Finite Volume (FV) schemes, often combined with implicit time-integration methods. While robust, these methods introduce much numerical diffusion depending on the number of grid points. In this paper we propose a high-order, space-time Discontinuous G...

In this paper we analyse different time integration methods for the two-fluid model and propose the BDF2 method as the preferred choice to simulate transient compressible multiphase flow in pipelines. Compared to the prevailing Backward Euler method, the BDF2 scheme has a significantly better accuracy (second order) while retaining the important pr...

This paper investigates the capability of the two-fluid model to predict the bubble drift velocity of elongated bubbles in channels. The two-fluid model is widely used in the oil and gas industry for dynamic multiphase pipeline simulations. The bubble drift velocity is an important quantity in predicting pipeline flushing and slug flow. In this pap...

Harlow and Welch [Phys. Fluids 8 (1965) 2182-2189] introduced a
discretization method for the incompressible Navier-Stokes
equations conserving the secondary quantities kinetic energy and
vorticity, besides the primary quantities mass and momentum. This method
was extended to fourth order accuracy by several researchers [25,14,21].
In this paper we...

Time integration of the incompressible Navier-Stokes equations with Runge-Kutta methods is not straightforward due to the differential-algebraic nature of the equations. In this work we investigate the temporal order of accuracy of velocity and pressure for both explicit and implicit methods. This is done by applying existing theory on Runge-Kutta...

This paper investigates the temporal accuracy of the velocity and pressure when explicit Runge–Kutta methods are applied to the incompressible Navier–Stokes equations. It is shown that, at least up to and including fourth order, the velocity attains the classical order of accuracy without further constraints. However, in case of a time-dependent gr...

In this paper we investigate energy-conserving time integration of the incompressible Navier-Stokes equations by employing linearly implicit Runge-Kutta methods. Such methods have the same order of accuracy and the same stability properties as fully nonlinear methods, but are much cheaper from a computational point of view. Numerical experiments sh...

This article reviews the state-of-the-art numerical calculation of wind turbine wake aerodynamics. Different computational fluid dynamics techniques for modeling the rotor and the wake are discussed. Regarding rotor modeling, recent advances in the generalized actuator approach and the direct model are discussed, as far as it attributes to the wake...

This article reviews the state of the art of the numerical calculation of wind-turbine wake aerodynamics. Different CFD techniques for modeling the rotor and the wake are discussed. Regarding rotor modeling, recent advances in the generalized actuator approach and the direct model are discussed, as far as it attributes to the wake description. For...

## Projects

Project (1)