Related papers: Computational p-Willmore Flow with Conformal Penal…
In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy…
A constraint penalization method is introduced within the Lattice Boltzmann (LBM) framework to model fluid-structure interactions involving rigid bodies. The proposed approach extends the fictitious domain concept by enforcing the…
We introduce a parametric framework for the study of Willmore gradient flows which enables to consider a general class of weak, energy-level solutions and opens the possibility to study energy quantization and finite-time singularities. We…
Active gel theory has recently been very successful in describing biologically active materials such as actin filaments or moving bacteria in temporally fixed and simple geometries such as cubes or spheres. Here we develop a computational…
We consider the exact penalization of the incompressibility condition $div(u)=0$ for the velocity field of a Bingham fluid in terms of the $L^1$-norm. This penalization procedure results in a nonsmooth optimization problem for which we…
We present the derivation of a new unidirectional model for We present the derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipes. We introduce a local reference frame to take into account the…
In this paper, we investigate the effect of boundary surface roughness on numerical simulations of incompressible fluid flow past a cylinder in two and three spatial dimensions furnished with slip boundary conditions. The governing…
We introduce action-driven flows for causal variational principles, being a class of non-convex variational problems emanating from applications in fundamental physics. In the compact setting, H\"older continuous curves of measures are…
The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…
Data-driven machine learning models often require extensive datasets, which can be costly or inaccessible, and their predictions may fail to comply with established physical laws. Current approaches for incorporating physical priors…
The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…
P-splines are penalized B-splines, in which finite order differences in coefficients are typically penalized with an $\ell_2$ norm. P-splines can be used for semiparametric regression and can include random effects to account for…
We adapt the statistical mechanics of the shallow-water equations to the case where the flow is forced at small scales. We assume that the statistics of forcing is encoded in a prior potential vorticity distribution which replaces the…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
This paper is concerned with diffuse-interface approximations of the Willmore flow. We first present numerical results of standard diffuse-interface models for colliding one dimensional interfaces. In such a scenario evolutions towards…
This is a companion paper to arXiv:1207.3529 where we introduced the spinorial energy functional and studied its main properties in dimensions equal or greater than three. In this article we focus on the surface case. A salient feature here…
This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent…
An improved one-dimensional mathematical model based on Pulsed Flow Equations (PFE) is derived by integrating the axial component of the momentum equation over the transient Womersley velocity profile, providing a dynamic momentum equation…
We present a generalized form of open boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving open or outflow boundaries. The generalized form represents a family of open boundary…
In this article we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be…