Related papers: Heuristical and numerical considerations for the c…
Numerical approximations of shock waves sometimes suffer from instabilities called carbuncles. Techniques for suppressing carbuncles are trial-and-error and lack in reliability and generality, partly because theoretical knowledge about…
The artificial viscosity approach for curing the carbuncle phenomenon (a numerical problem, also known as the shock instability) in shock-capturing methods has been recently presented and successfully tested on the first-order schemes in…
We investigate the numerical artifact known as a carbuncle, in the solution of the shallow water equations. We propose a new Riemann solver that is based on a local measure of the entropy residual and aims to avoid carbuncles while…
While traditional approaches to prevent the carbuncle phenomenon in gas dynamics simulations increase the viscosity on entropy and shear waves near shocks, it was quite recently suggested to instead decrease the viscosity on the acoustic…
We conjecture the exact shock statistics in the inviscid decaying Burgers equation in D>1 dimensions, with a special class of correlated initial velocities, which reduce to Brownian for D=1. The prediction is based on a field-theory…
We discuss the possibility that astrophysical accretion disks are dynamically unstable to non-axisymmetric disturbances with characteristic scales much smaller than the vertical scale height. The instability is studied using three methods:…
An important problem in gas dynamics simulation is to prevent the carbuncle, a breakdown of discrete shock profiles. We show that for high Froude number, this also occurs in shallow water simulations and give numerical evidence that all…
The first consistent model for the turbulent tachocline is presented, with the turbulent diffusivity computed within the model instead of being specified arbitrarily. For the origin of the 3D turbulence a new mechanism is proposed. Owing to…
We propose that statistical averages in relativistic turbulence exhibit universal properties. We consider analytically the velocity and temperature differences structure functions in the (1+1)-dimensional relativistic turbulence in which…
The condition of linear instability for a converging cylindrical shock wave in an arbitrary inviscid medium is obtained. The shape of resulting shock wave front is not changed significantly, but the restriction of energy cumulation can be…
We study experimentally the impulse response of a cylinder wake below the critical Reynolds number of the B\'enard-von K\'arm\'an instability. In this subcritical regime, a localized inhomogeneous region of convective instability exists…
This paper identifies a new pathology that can be found for numerical simulations of nonlinear conservation law systems. Many of the difficulties already identified in the literature (rarefaction shocks, carbuncle phenomena, slowly moving…
Shocks are ubiquitous in astrophysical sources, many of which involve relativistic bulk motions, leading to the formation of relativistic shocks. Such relativistic shocks have so far been studied mainly in one dimension, for simplicity, but…
Prediction is a fundamental objective of science. It is more difficult for chaotic and complex systems like turbulence. Here we use information theory to quantify spatial prediction using experimental data from a turbulent soap film. At…
We investigate inviscid numerical instabilities that arise in simulations of axisymmetric flow over a hypersonic sphere in an inert, calorically perfect gas at low specific heat ratio ($\gamma \approx 1.1$--$1.2$). We show that when the…
We present the first numerical analysis of causal, stable first-order relativistic hydrodynamics with ideal gas microphysics, based in the formalism developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK theory). The BDNK approach…
A parametric numerical study of three-dimensional instability of steady flows in a helical pipe of arbitrary curvature and torsion is carried out. The computations are performed by a numerical approach verified against independent…
The essence of shear instability is fully revealed both mathematically and physically. A general sufficient and necessary stable criterion is obtained analytically within linear context. It is the analogue of Kelvin-Arnol'd theorem, i.e.,…
Modern shock-capturing schemes often suffer from numerical shock anomalies if the flow field contains strong shocks, which may limit their further application in hypersonic flow computations. In the current study, we devote our efforts to…
In this paper, continuous research is undertaken to explore the underlying mechanism of numerical shock instabilities of Godunov-type schemes for strong shocks. By conducting dissipation analysis of Godunov-type schemes and a sequence of…