Related papers: A stabilized finite element method for a flow prob…
In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…
A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…
In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier-Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and…
Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…
We present the components of a high-order accurate Navier-Stokes solver designed to simulate high-Reynolds-number stratified flows. The proposed numerical model addresses some of the numerical and computational challenges that…
Most classical finite element schemes for the (Navier-)Stokes equations are neither pressure-robust, nor are they inf-sup stable on general anisotropic triangulations. A lack of pressure-robustness may lead to large velocity errors,…
In this study the numerical performance of the fourth order compact formulation of the steady 2-D incompressible Navier-Stokes equations introduced by Erturk et al. (Int. J. Numer. Methods Fluids, 50, 421-436) will be presented. The…
The resolution of the incompressible Navier-Stokes equations is tricky, and it is well known that one of the major issue is to compute a divergence free velocity. The non-conforming Crouzeix-Raviart finite element are convenient since they…
We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
We present a spectral element solver for the steady incompressible Navier-Stokes equations subject to a free surface. Utilizing the kinematic behaviour of the free surface boundary, an iterative pseudo-time procedure is proposed to…
Electrokinetic phenomena in nanopore sensors and microfluidic devices require accurate simulation of coupled fluid-electrostatic interactions in geometrically complex domains with irregular boundaries and adaptive mesh refinement. We…
The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche's method. Since the non-matching meshes can result in arbitrarily…
Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries…
For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based…
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…
The paper discusses a stabilization of a finite element method for the equations of fluid motion in a time-dependent domain. After experimental convergence analysis, the method is applied to simulate a blood flow in the right ventricle of a…
This paper presents a new numerical method for the compressible Navier-Stokes equations governing the flow of an ideal isentropic gas. To approximate the continuity equation, the method utilizes a discontinuous Galerkin discretization on…
In this paper we discretize the incompressible Navier-Stokes equations in the framework of finite element exterior calculus. We make use of the Lamb identity to rewrite the equations into a vorticity-velocity-pressure form which fits into…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…