Related papers: A spatially adaptive high-order meshless method fo…
We present a monolithic geometric multigrid preconditioner for solving fluid-solid interaction problems in Stokes limit. The problems are discretized by a spatially adaptive high-order meshless method, the generalized moving least squares…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
A parallel implementation of a compatible discretization scheme for steady-state Stokes problems is presented in this work. The scheme uses generalized moving least squares to generate differential operators and apply boundary conditions.…
We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime…
This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node…
Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…
Meshless methods inherently do not require mesh topologies and are practically used for solving continuum equations. However, these methods generally tend to have a higher computational load than conventional mesh-based methods because…
This article investigates matrix-free higher-order discontinuous Galerkin discretizations of the Navier--Stokes equations for incompressible flows with variable viscosity. The viscosity field may be prescribed analytically or governed by a…
We present a new meshless method for scalar diffusion equations which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of…
In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in [50] is a…
The boundary layer represents a fundamental structure in fluid dynamics, where accurate boundary discretization significantly enhances computational efficiency. This paper presents a third-order boundary discretization for compact…
Finite element discretization of Stokes problems can result in singular, inconsistent saddle point linear algebraic systems. This inconsistency can cause many iterative methods to fail to converge. In this work, we consider the lowest-order…
In this paper we present an efficient discretization method for the solution of the unsteady incompressible Navier-Stokes equations based on a high order (Hybrid) Discontinuous Galerkin formulation. The crucial component for the efficiency…
In (J. Comput. Phys., 417, 109577, 2020) we introduced a space-time embedded-hybridizable discontinuous Galerkin method for the solution of the incompressible Navier-Stokes equations on time-dependent domains of which the motion of the…
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features…
In this paper, we propose two monolithic fully discrete finite element methods for fluid-structure interaction (FSI) based on a novel Piola-type Arbitrary Lagrangian-Eulerian (ALE) mapping. For the temporal discretization, we apply the…
We propose a new first-order-system least squares (FOSLS) finite-element discretization for singularly perturbed reaction-diffusion equations. Solutions to such problems feature layer phenomena, and are ubiquitous in many areas of applied…
One of the main challenges in numerically solving partial differential equations is finding a discretisation for the computational domain that balances the accurate representation of the underlying field with computational efficiency.…
In this work, we introduce a novel computational framework for solving the two-dimensional Hele-Shaw free boundary problem with surface tension. The moving boundary is represented by point clouds, eliminating the need for a global…