相关论文: On numerical stabilization in modeling double-diff…
This paper focuses on identifying the cause and proposing a remedy for the problem of spurious pressure oscillations in a sharp-interface immersed boundary finite element method for incompressible flow problems in moving domains. The…
We present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations…
Extending results of Oh and Zumbrun in dimensions $d\ge 3$, we establish nonlinear stability and asymptotic behavior of spatially-periodic traveling-wave solutions of viscous systems of conservation laws in critical dimensions $d=1,2$,…
This paper is the fifth in a series exploring the physical consequences of the solidity of glass-forming liquids. Paper IV proposed a model where the density field is described by a time-dependent Ginzburg-Landau equation of the…
Geometric flux-based Volume-of-Fluid (VOF) methods are widely considered consistent in handling two-phase flows with high density ratios. However, although the conservation of mass and momentum is consistent for two-phase incompressible…
We present a theoretical analysis of the dynamic structure factor (DSF) of a liquid at and below the mode coupling critical temperature $T_c$, by developing a self-consistent theoretical treatment which includes the contributions both from…
Modeling flow through porous media with multiple pore-networks has now become an active area of research due to recent technological endeavors like geological carbon sequestration and recovery of hydrocarbons from tight rock formations.…
The efficient and reliable approximation of convection-dominated problems continues to remain a challenging task. To overcome the difficulties associated with the discretization of convection-dominated equations, stabilization techniques…
The numerical simulation of the inviscid Burgers' equation is often hindered by spurious oscillations near discontinuities. To mitigate this issue, a viscous term can be introduced, leading to the viscous Burgers' equation. In this work,…
In the present study, MHD boundary layer flow with heat and mass transfer of a nanofluid with viscous dissipation over a non-linear stretching sheet embedded in a porous medium is studied. The governing non-linear partial differential…
We employ a canonical variational framework for the predictive characterization of structural instabilities that develop during the diffusion-driven transient swelling of hydrogels under geometrical constraints. The variational formulation…
We consider systematic numerical approximation of a viscoelastic phase separation model that describes the demixing of a polymer solvent mixture. An unconditionally stable discretisation method is proposed based on a finite element…
Mathematical models for flow through porous media typically enjoy the so-called maximum principles, which place bounds on the pressure field. It is highly desirable to preserve these bounds on the pressure field in predictive numerical…
In this note we aim at a characterisation of the discretisation of viscous dissipation which allows to distinguish `physical' (also frequently called `molecular', or `resolved') from `numerical' dissipation in DG-discretised incompressible…
The effects of a "diffusing diffusivity" (DD), a stochastically time-varying diffusion coefficient, are explored within the frameworks of three different forms of fractional Brownian motion (FBM): (i) the Langevin equation driven by…
This study presents a fractional-order continuum mechanics approach that allows combining selected characteristics of nonlocal elasticity, typical of classical integral and gradient formulations, under a single frame-invariant framework.…
We investigate the numerical performance of a Discontinuous Galerkin (DG) hydrodynamics implementation when applied to the problem of driven, isothermal supersonic turbulence. While the high-order element-based spectral approach of DG is…
This paper addresses the variational multiscale stabilization of standard finite element methods for linear partial differential equations that exhibit multiscale features. The stabilization is of Petrov-Galerkin type with a standard finite…
Viscoelastic flows occur widely, and numerical simulations of them are important for a range of industrial applications. Simulations of viscoelastic flows are more challenging than their Newtonian counterparts due to the presence of…
This study presents the analytical formulation and the finite element solution of fractional order nonlocal plates under both Mindlin and Kirchoff formulations. By employing consistent definitions for fractional-order kinematic relations,…