Related papers: Adaptive finite difference methods for the Willmor…
We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, rather than the…
The main contribution of this paper is the formulation of a diffuse approximation method(DAM), for two-dimensional channel flows. The proposed method is based on the vorticity-streamfunction formulation. The DAM which estimates derivates of…
This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a…
Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods produce accurate solutions and numerical convergence can be demonstrated using a resolution…
In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…
We consider the vertex-centered finite volume method with first-order conforming ansatz functions. The adaptive mesh-refinement is driven by the local contributions of the weighted-residual error estimator. We prove that the adaptive…
We present a high order one-step ADER-WENO finite volume scheme with space-time adaptive mesh refinement (AMR) for the solution of the special relativistic hydrodynamic and magnetohydrodynamic equations. By adopting a local discontinuous…
This work presents a robust and efficient sharp interface immersed boundary (IBM) framework, which is applicable for all-speed flow regimes and is capable of handling arbitrarily complex bodies (stationary or moving). The work deploys an…
We present a hybrid method combining a minimizing movement scheme with neural operators for the simulation of phase field-based Willmore flow. The minimizing movement component is based on a standard optimization problem on a regular grid…
A comprehensive scheme for the spatial discretisation of continuity equation, momentum advection and normal and shear stresses at the fluid interfaces is presented for numerically simulating the incompressible two phase flows based on the…
Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high…
Parametric finite elements lead to very efficient numerical methods for surface evolution equations. We introduce several computational techniques for curvature driven evolution equations based on a weak formulation for the mean curvature.…
We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…
An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally…
A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the…
We present the extension of an efficient and highly parallelisable framework for incompressible fluid flow simulations to viscoplastic fluids. The system is governed by incompressible conservation of mass, the Cauchy momentum equation and a…
This work introduces a novel adaptive central-upwind scheme designed for simulating compressible flows with discontinuities in the flow field. The proposed approach offers significant improvements in computational efficiency over the…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
We propose and analyze stable finite element approximations for Willmore flow of planar curves. The presented schemes are based on a novel weak formulation which combines an evolution equation for curvature with the curvature formulation…
We model incompressible flows with an adaptive stabilized finite element method Stokes flows, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers…