Related papers: On numerical stabilization in modeling double-diff…
Finger-type convection in double-diffusive instability (DDI) controls mixing and scalar transport in many stratified flows, yet a quantitative, finger-resolved description of the transient growth, transport, and saturation pathways has been…
The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth's crust, taking into account of both the elastic properties of rocks and the…
Global stabilization of viscous Burgers' equation around constant steady state solution has been discussed in the literature. The main objective of this paper is to show global stabilization results for the 2D forced viscous Burgers'…
When a more mobile fluid displaces another immiscible one in a porous medium, viscous fingering propagates with a partial sweep, which hinders oil recovery and soil remedy. We experimentally investigate the feasibility of tuning such…
Fingering double diffusive convection with real seawater properties is studied by two-dimensional direct numerical simulations for the wall-bounded domain and compared with the results for fully periodic domain. For fixed unstable salinity…
Vertically bounded fingering double diffusive convection (DDC) is numerically investigated, focusing on the influences of different velocity boundary conditions, i.e. the no-slip condition which is inevitable in the lab-scale experimental…
We present experiments and theory describing the transition from viscosity-stabilized flow to gravitationally unstable fingering for two-phase flow in a 3D synthetic porous medium. Observation is made possible by the use of our newly…
Divergence and vorticity damping, which operate upon horizontal divergence and relative vorticity, are explicit diffusion mechanisms used in dynamical cores to ensure stability. To avoid numerical blow-up from excessively strong diffusion,…
The results from a series of well characterised, unstable, miscible displacement experiments in a Hele Shaw cell with a quarter five-spot source-sink geometry are presented, with comparisons to detailed numerical simulation. We perform…
To find the regularities of formed fingers in gravity driven coating flows on upper cylinder and sphere, the mathematical formulation to model the fingering instability on cylindrical or spherical surface which consists of a capillary wave…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
In this article, global stabilization results for the two dimensional (2D) viscous Burgers' equation, that is, convergence of unsteady solution to its constant steady state solution with any initial data, are established using a nonlinear…
We analyze experimental data on double diffusive convection in an electrochemical cell in the finger regime. All fingers in the experiments are bounded on at least one end by a solid wall. The properties of these fingers are compared with…
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…
Direct numerical simulations are conducted for double diffusive convection (DDC) bounded by two parallel plates, with fluid properties similar to the values of seawater. The DDC flow is driven by an unstable salinity difference and…
We present a novel hyperviscosity formulation for stabilizing RBF-FD discretizations of the advection-diffusion equation. The amount of hyperviscosity is determined quasi-analytically for commonly-used explicit, implicit, and…
We derive a variational multiscale (VMS) finite element formulation for a viscoelastic, tensor-based blood damage model. The tensor equation is numerically stabilized by a logarithmic shape tensor description that prevents unphysical,…
We present a new hyperviscosity formulation for stabilizing radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion-reaction equations on manifolds $\mathbb{M} \subset \mathbb{R}^3$ of co-dimension one. Our…
We perform three-dimensional numerical simulations to understand the role of viscous fingering in sweeping a high-viscous fluid (HVF). These fingers form due to the injection of a low-viscous fluid (LVF) into a porous media containing the…
In this paper we consider modifications to Darcy's equation wherein the drag coefficient is a function of pressure, which is a realistic model for technological applications like enhanced oil recovery and geological carbon sequestration. We…