Related papers: Computational p-Willmore Flow with Conformal Penal…
A new numerical method is presented for solving the rotating shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical…
Accurately, efficiently, and stably computing complex fluid flows and their evolution near solid boundaries over long horizons remains challenging. Conventional numerical solvers require fine grids and small time steps to resolve near-wall…
We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable…
We introduce and analyze a Statically Condensed Iterated Penalty (SCIP) method for solving incompressible flow problems discretized with $p$th-order Scott-Vogelius elements. While the standard iterated penalty method is often the preferred…
In this article we present a goal-oriented adaptive finite element method for a class of subsurface flow problems in porous media, which exhibit seepage faces. We focus on a representative case of the steady state flows governed by a…
A formulation of the immersed boundary method for incompressible flow over bodies with surface slip described by the Navier boundary condition is presented. In the present method, the wall slip velocity and the boundary force are determined…
There are very few results on mixed finite element methods on surfaces. A theory for the study of such methods was given recently by Holst and Stern, using a variational crimes framework in the context of finite element exterior calculus.…
On a closed Riemannian surface $(M,\bar g)$ with negative Euler characteristic, we study the problem of finding conformal metrics with prescribed volume $A>0$ and the property that their Gauss curvatures $f_\lambda= f + \lambda$ are given…
In this article, the author investigates flow lines of the classical Willmore flow, which start to move in a smooth parametrization of a Hopf-torus in $\mathbb{S}^3$. We prove that any such flow line of the Willmore flow exists globally, in…
We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for…
Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
In this work, we develop a modelling framework for granular flows based on the shallow water moment equations on inclined planes. Under the assumption of a polynomial expansion of the velocity field, the model extends the classical shallow…
This paper presents a general and robust method for the fluid-structure interaction of membranes and shells undergoing large displacement and large added-mass effects by coupling an immersed-boundary method with a shell finite-element…
The paper is devoted to the variational analysis of the Willmore, and other L^2 curvature functionals, among immersions of 2-dimensional surfaces into a compact riemannian m-manifold (M^m,h) with m>2. The goal of the paper is twofold, on…
We consider the surface diffusion and Willmore flows acting on a general class of (possibly non-compact) hypersurfaces parameterized over a uniformly regular reference manifold possessing a tubular neighborhood with uniform radius. The…
The volume penalty method provides a simple, efficient approach for solving the incompressible Navier-Stokes equations in domains with boundaries or in the presence of moving objects. Despite the simplicity, the method is typically limited…
This article investigates stationary surfaces with boundaries, which arise as the critical points of functionals dependent on curvature. Precisely, a generalized "bending energy" functional $\mathcal{W}$ is considered which involves a…
In this paper we consider surfaces which are critical points of the Willmore functional subject to constrained area. In the case of small area we calculate the corrections to the intrinsic geometry induced by the ambient curvature. These…
We present and test a general-purpose code, called PPASPH, for evolving self-gravitating fluids in astrophysics, both with and without a collisionless component. In PPASPH, hydrodynamical properties are computed by using the SPH (Smoothed…