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The study of the Euler equations in flows with constant vorticity has piqued the curiosity of a considerable number of researchers over the years. Much research has been conducted on this subject under the assumption of steady flow. In this…
We extend the linear analysis of the drag instability in a 1D perpendicular isothermal C-shock by Gu & Chen to 2D perpendicular and oblique C-shocks in the typical environment of star-forming clouds. Simplified dispersion relations are…
The Gaussian-filtered Navier-Stokes equations are examined theoretically and a generalized theory of their numerical stability is proposed. Using the exact expansion series of subfilter-scale stresses or integration by parts, the terms…
Elastic properties and internal states of isotropic sphere packings are studied by numerical simulations. Several numerical protocols to assemble dense configurations are compared. One, which imitates experiments with lubricated contacts,…
We introduce non conforming virtual elements to approximate the eigenvalues and eigenfunctions of the two dimensional acoustic vibration problem. We focus our attention on the pressure formulation of the acoustic vibration problem in order…
We perform fully general relativistic simulations of rotating stellar core collapse in three spatial dimension. A parametric equation of state is adopted following Dimmelmeier et al. The early stage of the collapse is followed by an…
Temporal decorrelations in compressible isotropic turbulence are studied using the space-time correlation theory and direct numerical simulation. A swept-wave model is developed for dilatational components while the classic random sweeping…
Thermoacoustic instabilities in can-annular combustors of stationary gas turbines lead to unstable Bloch modes which appear as rotating acoustic pressure waves along the turbine annulus. The multi-scale, multiphysical nature of the full…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
Periodic traveling waves are numerically computed in a constant vorticity flow subject to the force of gravity. The Stokes wave problem is formulated via a conformal mapping as a nonlinear pseudo-differential equation, involving a periodic…
The shock instability problem commonly arises in flow simulations involving strong shocks, particularly when employing high-order schemes, limiting their applications in hypersonic flow simulations. This study focuses on exploring the…
Moving grids are of interest in the numerical solution of hydrodynamical problems and in numerical relativity. We show that conventional integration methods for the simple wave equation in one and more than one dimension exhibit a number of…
A numerical analysis of the effect of artificial viscosity is undertaken in order to understand the effect of numerical diffusion on numerical boundary feedback control. The analysis is undertaken on the linear hyperbolic systems…
We give computational results to study the accuracy of several quasicontinuum methods for two benchmark problems - the stability of a Lomer dislocation pair under shear and the stability of a lattice to plastic slip under tensile loading.…
The comparative study of two globally convergent numerical methods for acoustic tomography is carried out in two dimensions. These are the boundary control method and the quasi-reversibility method. The novelty is that in the latter a…
The linear stability of isothermal Bondi accretion with a shock is studied analytically in the asymptotic limit of high incident Mach number M_1. The flow is unstable with respect to radial perturbations as expected by Nakayama (1993), due…
Two-dimensional Stokes flow with injection and suction is investigated through a second-order, perturbative mode-coupling approach. We examine the time-dependent disturbance of an initially circular interface separating two viscous fluids,…
We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…
Many dynamic pipe flow simulator tools are capable of predicting the onset of hydrodynamic flow instability through detailed simulation. These instabilities provide a natural mechanism for flow regime transition. The quality and reliability…
In this paper, we study random dissipative weak solutions of the compressible Euler equations in the Kelvin-Helmholtz (KH) instability. Motivated by the fact that weak entropy solutions are not unique and can be viewed as inviscid limits of…