Related papers: Asymptotic-analysis-inspired boundary conditions a…
This paper presents a more stable implementation and a highly accurate numerical tool for predicting flooding in urban areas. We started with the (linearised) well-posedness analysis by [1], where far-field boundary conditions were proposed…
Dissipative particle dynamics (DPD) is an effective mesoscopic particle model with a lower computational cost than molecular dynamics because of the soft potentials that it employs. However, the soft potential is not strong enough to…
Numerical simulation of viscoelastic flows is challenging because of the hyperbolic nature of viscoelastic constitutive equations. Despite their superior accuracy and efficiency, pseudo-spectral methods require the introduction of…
Forming macroscopic solid bodies in circumstellar discs requires local dust concentration levels significantly higher than the mean. Interactions of the dust particles with the gas must serve to augment local particle densities, and…
Even though the Dissipative Particle Dynamics (DPD) has shown its worth in a variety of research areas, it has been rarely used for polymer dynamics, particularly in dilute and semi-dilute conditions and under imposed flow fields. For such…
We consider the compressible barotropic Navier-Stokes equations in a half-line and study the time-asymptotic behavior toward the outgoing viscous shock wave. Precisely, we consider the two boundary problems: impermeable wall and inflow…
This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--diffusion--advection equation. By using an asymptotic…
Consider the unsteady neutron transport equation with diffusive boundary condition in 2D convex domains. We establish the diffusive limit with both initial layer and boundary layer corrections. The major difficulty is the lack of regularity…
A well-developed method to induce mixing on microscopic scales is to exploit flows generated by steady streaming. Steady streaming is a classical fluid dynamics phenomenon whereby a time-periodic forcing in the bulk or along a boundary is…
This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…
We theoretically and numerically investigate the instabilities driven by diffusiophoretic flow, caused by a solutal concentration gradient along a reacting surface. The important control parameter is the Peclet number Pe, which quantifies…
This paper introduces a novel dynamical pressure boundary condition for weakly-compressible smoothed particle hydrodynamics (WCSPH). Unlike previous methods that rely on indirect approaches or ghost particles, our method integrates the…
This work discusses the correct modeling of the fully nonlinear free surface boundary conditions to be prescribed in water waves flow simulations based on potential flow theory. The main goal of such a discussion is that of identifying a…
Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference (FD) methods used to model such phenomena. Methods currently detailed…
In this paper we consider the global stability of solutions of an affine stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
We discuss how matrix-free/timestepper algorithms can efficiently be used with dynamic non-Newtonian fluid mechanics simulators in performing systematic stability/bifurcation analysis. The timestepper approach to bifurcation analysis of…
3D-0D coupled flow models are widely used across many application fields but remain challenging to solve. Implicit coupling introduces non-local terms, whereas explicit coupling results in only conditionally stable schemes. Furthermore,…
In this paper, we investigate the effect of boundary surface roughness on numerical simulations of incompressible fluid flow past a cylinder in two and three spatial dimensions furnished with slip boundary conditions. The governing…
The semi-analytical wall boundary conditions present a mathematically rigorous framework to prescribe the influence of solid walls in SPH for fluid flows. In this paper they are investigated with respect to the skew-adjoint property which…
This paper addresses the derivation of generic and tractable sufficient conditions ensuring the stability of a coupled system composed of a reaction-diffusion partial differential equation (PDE) and a finite-dimensional linear time…