Related papers: The Variational Multiscale Formulation for the Ful…
In this study, a stabilized finite element analysis of unified Stokes-Darcy-Brinkman system fully coupled with variable coefficient Advection-Diffusion-Reaction equation(VADR) has been carried out. The viscosity of the fluid, involved in…
The problem of multiphase materials (fluid or solid) interacting with the rigid body structure is studied by proposing a novel VMS-FEM (variational multi-scale finite element method) in the Eulerian framework using the fixed mesh. The…
This paper presents the construction of novel stabilized finite element methods in the convective-diffusive context that exhibit correct-energy behavior. Classical stabilized formulations can create unwanted artificial energy. Our…
Standard Virtual Element Methods (VEM) are based on polynomial projections and require a stabilization term to evaluate the contribution of the non-polynomial component of the discrete space. However, the stabilization term is not uniquely…
A semi-implicit, residual-based variational multiscale (VMS) formulation is developed for the incompressible Navier--Stokes equations. The approach linearizes convection using an extrapolated (Oseen-type) convecting velocity, producing a…
In this study a stabilized finite element method for solving advection-diffusion-reaction equation with spatially variable coefficients has been carried out. Here subgrid scale approach along with algebraic approximation to the sub-scales…
One of the more promising recent approaches to turbulence modelling is the Variational Multiscale Large Eddy Simulation (VMS LES) method proposed by Hughes et al. [Comp. Visual. Sci., vol. 3, pp. 47-59, 2000]. This method avoids several…
Logarithmic conformation reformulations for viscoelastic constitutive laws have alleviated the high Weissenberg number problem, and the exploration of highly elastic flows became possible. However, stabilized formulations for logarithmic…
In this article, we extend the Variational Multi-scale method with spectral approximation of the sub-scales to two-dimensional advection-diffusion problems. The spectral VMS method is cast for low-order elements as a standard VMS method…
In this work, we introduce a Variational Multi-Scale (VMS) method for the numerical approximation of parabolic problems, where sub-grid scales are approximated from the eigenpairs of associated elliptic operator. The abstract method is…
We present the design, convergence analysis and numerical investigations of the nonconforming virtual element method with Streamline Upwind/Petrov-Galerkin (VEM-SUPG) stabilization for the numerical resolution of…
A linear stability analysis of an elastic surface immersed in a viscous fluid is presented. The coupled system is modeled using the method of regularized Stokeslets (MRS), a Lagrangian method for simulating fluid-structure interaction at…
An adjoint-based variational optimal mixed model (VOMM) is proposed for subgrid-scale (SGS) closure in large-eddy simulation (LES) of turbulence. The stabilized adjoint LES equations are formulated by introducing a minimal regularization to…
We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent…
We propose a mathematical model that combines elastic, viscous and porous effects with growth or shrinkage due to microstructural changes. This phenomenon is important in tissue or tumor growth, as well as in dermal contraction. Although…
This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear problems. We build on the concept of an optimal projector defined…
A firm understanding and control of viscous fingering (VF) and miscible displacement will be vital to a wide range of industrial, environmental, and pharmaceutical applications, such as geological carbon-dioxide sequestration, enhanced oil…
We address the issue of designing robust stabilization terms for the nonconforming virtual element method. To this end, we transfer the problem of defining the stabilizing bilinear form from the elemental nonconforming virtual element…
We formulate a stabilized quasi-optimal Petrov-Galerkin method for singularly perturbed convection-diffusion problems based on the variational multiscale method. The stabilization is of Petrov-Galerkin type with a standard finite element…
In this paper we have studied subgrid multiscale stabilized formulation with dynamic subscales for non-Newtonian Casson fluid flow model tightly coupled with variable coefficients ADR ($VADR$) equation. The Casson viscosity coefficient is…