Related papers: A Novel Regularization for Higher Accuracy in the …
Several approaches are discussed how to understand the solution of the Dirichlet problem for the Poisson equation when the Dirichlet data are non-smooth such as if they are in $L^2$ only. For the method of transposition (sometimes called…
A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving $p$-Laplacian is offered. The governing systems of equations are based on steady incompressible flow of a Newtonian fluids. This paper…
Finite difference method was extended to unstructured meshes to solve Euler equations. The spatial discretization is made of two steps. First, numerical fluxes are computed at the middle point of each edge with high order accuracy. In this…
A modified Reynolds equation governing the steady flow of a fluid with low Reynolds number through a curvilinear, narrow tube, with its derivation from Stokes equations through asymptotic methods is presented. The channel considered may…
In this paper we present approaches that address two issues that can occur when the level-set method is used to simulate two-fluid flows in engineering practice. The first issue concerns regularizing the Heaviside function on arbitrary…
The swimming of a spheroid immersed in a viscous fluid and performing surface deformations periodically in time is studied on the basis of Stokes equations of low Reynolds number hydrodynamics. The average over a period of time of the…
Ideal systems like MHD and Euler flow may develop singularities in vorticity (w = curl v). Viscosity and resistivity are dissipative regularizations. We propose a minimal, local, conservative, nonlinear, dispersive regularization of…
Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical…
The classical no-slip boundary condition of the Navier-Stokes equations fails to describe the spreading motion of a droplet on a substrate due to the missing small-scale physics near the contact line. In this thesis, we introduce a novel…
In this paper, we consider the Stokes equations with non-homogeneous free boundary conditions, which is obtained by the linearization procedure of the free boundary problem of the Navier-Stokes equations describing the viscous compressible…
We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity. For this problem, the classical finite elements method of degree one converges only to order one-half for the L2 norm of the vorticity. We…
A new reformulation of a free boundary problem for the Stokes equations governing a viscous flow with overdetermined condition on the free boundary is proposed. The idea of the method is to transform the governing equations to a boundary…
Numerical and experimental studies have demonstrated the drag-reducing potential of carefully designed streamwise-elongated riblets in lowering skin-friction drag. To support the systematic design of such surface corrugations, recent…
This paper establishes strong convergence rates for the spatial finite element discretization of a two-dimensional stochastic Navier--Stokes system with transport noise and no-slip boundary conditions on a convex polygonal domain. The main…
Using the T-coercivity theory as advocated in [Chesnel, Ciarlet, T -coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients (2013)], we propose a new variational formulation of the…
In this paper, we treat the corner singularity expansion and its convergence result regarding the penalized system obtained by eliminating the pressure variable in the Stokes problem of incompressible flow. The penalized problem is a kind…
A volume penalization-based immersed boundary technique is developed and thoroughly validated for fluid flow problems, specifically flow over bluff bodies. The proposed algorithm has been implemented in an Open Source Field Operation and…
We construct and analyze a strongly consistent second-order finite difference scheme for the steady two-dimensional Stokes flow. The pressure Poisson equation is explicitly incorporated into the scheme. Our approach suggested by the first…
Mapping between discrete and continuous distributions is a difficult task and many have had to resort to heuristical approaches. We propose a tessellation-based approach that directly learns quantization boundaries in a continuous space,…
We investigate a level-set type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable…