Related papers: Modeling transitional plane Couette flow
We consider the dynamic Biot model describing the interaction between fluid flow and solid deformation including wave propagation phenomena in both the liquid and solid phases of a saturated porous medium. The model couples a hyperbolic…
This chapter reviews and compares discontinuous Galerkin time-stepping methods for the numerical approximation of second-order ordinary differential equations, particularly those stemming from space finite element discretization of wave…
We describe in detail a recently proposed lattice-Boltzmann model for simulating flows with multiple phases and components. In particular, the focus is on the modeling of one-component fluid systems which obey non-ideal gas equations of…
Using Monte Carlo simulation we investigated time of flight current transients predicted by the dipolar glass model for a random spatial distribution of hopping centers. Behavior of the carrier drift mobility was studied at room temperature…
We present a class of Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for the incompressible flow with moving boundaries and interfaces including two-phase flow with surface tension.
We present a new method for simulating incompressible immiscible two-phase flow in porous media. The semi-implicit method decouples the wetting phase pressure and saturation equations. The equations are discretized using a hybridizable…
In this paper, we focus on designing a well-conditioned Glarkin spectral methods for solving a two-sided fractional diffusion equations with drift, in which the fractional operators are defined neither in Riemann-Liouville nor Caputo sense,…
In plane Couette flow, the incompressible fluid between two plane parallel walls is driven by the motion of those walls. The laminar solution, in which the streamwise velocity varies linearly in the wall-normal direction, is known to be…
Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The method takes advantage of multilevel structure in expansions…
We develop an approach for simulating acousto-elastic wave phenomena, including scattering from fluid-solid boundaries, where the solid is allowed to be anisotropic, with the Discontinuous Galerkin method. We use a coupled first-order…
In this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining…
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, based on piecewise constant polynomials is formulated for…
This paper focuses on the adaptive discontinuous Galerkin (DG) methods for the tempered fractional (convection) diffusion equations. The DG schemes with interior penalty for the diffusion term and numerical flux for the convection term are…
As an extension of our previous work in Sun et.al (2018) [41], we develop a discontinuous Galerkin method for solving cross-diffusion systems with a formal gradient flow structure. These systems are associated with non-increasing entropy…
Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffusion-reaction models arise as solutions to the associated…
A diffused-interface approach based on the Allen-Cahn phase field equation is developed within a high-order Discontinuous Galerkin framework. The interface capturing technique is based on the balance between explicit diffusion and…
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…
Numerical calculations of vortex flows in Taylor-Couette systems with counter rotating cylinders are presented. The full, time dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method.…
In the frame of the traditional wavelet-Galerkin method based on the compactly supported wavelets, it is important to calculate the so-called connection coefficients that are some integrals whose integrands involve products of wavelets,…