21 citations · 79 across the 17 of their papers we have counts for
17 papers
A thermodynamically consistent framework for finite growth of multi-constituent mixtures with application to tumor growth
Jonathan Stollberg, Marco F. P. ten Eikelder, Dominik Schillinger
Biological tissues grow by continuously producing, transporting, and reorganizing multiple interacting constituents. These processes are intrinsically coupled to finite deformation…
Surface-tension calibration for N-phase mixtures
M. F. P. ten Eikelder, A. Brunk
Diffuse-interface (phase-field) models are a widely used framework for interfacial dynamics in complex fluids, in which sharp interfaces are replaced by smooth transition layers an…
Symmetric structure-preserving discretization of N-phase incompressible fluid mixtures with arbitrary density ratios
M. F. P. ten Eikelder, A. Brunk
Diffuse-interface models are a widely used framework for interfacial dynamics in complex fluids, in which interfaces are represented through smooth transition layers and capillary…
An entropy-stable and kinetic energy-preserving macro-element HDG method for compressible flows
Vahid Badrkhani, Marco F. P. ten Eikelder, Dominik Schillinger
This paper introduces a high order numerical framework for efficient and robust simulation of compressible flows. To address the inefficiencies of standard hybridized discontinuous…
A unified framework for N-phase Navier-Stokes Cahn-Hilliard Allen-Cahn mixture models with non-matching densities
M. F. P. ten Eikelder
Over the past few decades, numerous N-phase incompressible diffuse-interface flow models with non-matching densities have been proposed. Despite aiming to describe the same physics…
The matrix-free macro-element hybridized Discontinuous Galerkin method for steady and unsteady compressible flows
Vahid Badrkhani, Marco F. P. ten Eikelder, Rene R. Hiemstra +1
The macro-element variant of the hybridized discontinuous Galerkin (HDG) method combines advantages of continuous and discontinuous finite element discretization. In this paper, we…
The divergence-free velocity formulation of the consistent Navier-Stokes Cahn-Hilliard model with non-matching densities, divergence-conforming discretization, and benchmarks
M. ten Eikelder, D. Schillinger
The prototypical diffuse-interface model that describes multi-component flows is the Navier-Stokes Cahn-Hilliard model (NSCH). Over the last decades many NSCH models have appeared…
Matrix-free polynomial preconditioning of saddle point systems using the hyper-power method
Michał Łukasz Mika, Marco ten Eikelder, Dominik Schillinger +1
This study explores the integration of the hyper-power sequence, a method commonly employed for approximating the Moore-Penrose inverse, to enhance the effectiveness of an existing…
Connecting continuum poroelasticity with discrete synthetic vascular trees for modeling liver tissue
Adnan Ebrahem, Etienne Jessen, Marco F. P. ten Eikelder +3
Computational simulations have the potential to assist in liver resection surgeries by facilitating surgical planning, optimizing resection strategies, and predicting postoperative…
Constraints for eliminating the Gibbs phenomenon in finite element approximation spaces
M. ten Eikelder, S. Stoter, Y. Bazilevs +1
One of the major challenges in finite element methods is the mitigation of spurious oscillations near sharp layers and discontinuities known as the Gibbs phenomenon. In this articl…
Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids
M. ten Eikelder, K. van der Zee, D. Schillinger
In this paper we derive a class of thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids. The class of mixture models is fully compa…
A unified framework for Navier-Stokes Cahn-Hilliard models with non-matching densities
M. ten Eikelder, K. van der Zee, I. Akkerman +1
Over the last decades, many diffuse-interface Navier-Stokes Cahn-Hilliard models with non-matching densities have appeared in the literature. These models claim to describe the sam…
Isogeometric analysis of linear free-surface potential flow
I. Akkerman, J. H. A. Meijer, M. ten Eikelder
This paper presents a novel variational formulation to simulate linear free-surface flow. The variational formulation is suitable for higher-order finite elements and higher-order…
An acoustic-convective splitting-based approach for the Kapila two-phase flow model
M. ten Eikelder, F. Daude, B. Koren +1
In this paper we propose a new acoustic-convective splitting-based numerical scheme for the Kapila five-equation two-phase flow model. The splitting operator decouples the acoustic…
Toward free-surface flow simulations with correct energy evolution: an isogeometric level-set approach with monolithic time-integration
I. Akkerman, M. ten Eikelder
This paper presents a new monolithic free-surface formulation that exhibits correct kinetic and potential energy behavior. We focus in particular on the temporal energy behavior of…
Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. II: The incompressible Navier-Stokes equations
M. Ten Eikelder, I. Akkerman
This paper presents the construction of a correct-energy stabilized finite element method for the incompressible Navier-Stokes equations. The framework of the methodology and the c…
Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective-diffusive context
M. ten Eikelder, I. Akkerman
This paper presents the construction of novel stabilized finite element methods in the convective-diffusive context that exhibit correct-energy behavior. Classical stabilized formu…