Related papers: Time integration and steady-state continuation for…
We study the large time behavior of the solutions to a two phase extension of the porous medium equation, which models the so-called seawater intrusion problem. The goal is to identify the self-similar solutions that correspond to steady…
When a thin liquid film flows down on a vertical fiber, one can observe the complex and captivating interfacial dynamics of an unsteady flow. Such dynamics are applicable in various fluid experiments due to their high surface area-to-volume…
A gradient dynamics model based on an extended interface Hamiltonian is presented that is able to describe the dynamics of structuring processes in thin films of liquid mixtures, solutions and suspensions on solid substrates including…
With the aim of establishing a criterion for identifying when a lipid bilayer has reached steady state using the molecular dynamics simulation technique, lipid bilayers of different composition in their liquid crystalline phase were…
Similar to the notion of h-adaptivity, where the discretization resolution is adaptively changed, I propose the notion of model adaptivity, where the underlying model (the governing equations) is adaptively changed in space and time.…
We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed…
We analyze a linear 3D/3D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic plate-like structure with the aim of deriving a simplified reduced model. Based on suitable energy dissipation…
The solidification and macro-segregation problem involving unsteady multi-physics and multi-phase fields is typically a complex process with mass, momentum, heat, and species transfers among solid, mushy, and liquid phase regions. The…
We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of…
Path-integral-based molecular dynamics (MD) simulations are widely used for the calculation of numerically exact quantum Boltzmann properties and approximate dynamical quantities. A nearly universal feature of MD numerical integration…
Analysing the dynamics of phase-changing liquid films is essential for enhancing the performance of thermal management systems. Still, direct simulation of the full governing equations is computationally expensive. To circumvent this…
A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…
For time integration of transient eddy current problems commonly implicit time integration methods are used, where in every time step one or several nonlinear systems of equations have to be linearized with the Newton-Raphson method due to…
A lubrication model can be used to describe the dynamics of a weakly volatile viscous fluid layer on a hydrophobic substrate. Thin layers of the fluid are unstable to perturbations and break up into slowly evolving interacting droplets. A…
Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for…
The equations in conservative form for nonlinear waves modeling on a liquid film flowing down a vertical plane have been investigated. It has been found that in the computational domain extended along the transverse axis the equations with…
Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the…
Melting and solidification processes are often affected by natural convection of the liquid, posing a multi-physics problem involving fluid flow, convective and diffusive heat transfer, and phase-change reactions. Enthalpy methods formulate…
The simulation of viscoelastic time-evolution problems described by a large number of internal variables and with a large spectrum of relaxation times requires high computational resources for their resolution. Furthermore, the internal…
We present a novel thermodynamically guided, low-noise, time-scale bridging, and pertinently efficient strategy for the dynamic simulation of microscopic models for complex fluids. The systematic coarse-graining method is exemplified for…