相关论文: Further studies on numerical instabilities of Godu…
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…
Numerical shock instability is a complexity which may occur in supersonic simulations. Riemann solver is usually the crucial factor that affects both the computation accuracy and numerical shock stability. In this paper, several classical…
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…
Godunov type numerical schemes for the class of hyperbolic systems, admitting non-classical $\delta-$ shocks are proposed. It is shown that the numerical approximations converge to the solution and preserve the physical properties of the…
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…
The paper presents a new approach of stability evaluation of the approximate Riemann solvers based on the direct Lyapunov method. The present methodology offers a detailed understanding of the origins of numerical shock instability in the…
Strong discontinuities in solutions of the gas dynamic equations under isentropic conditions, i.e., with continuity of entropy at the discontinuity, are examined. Solutions for a standard shock wave with continuity of energy at the…
Previous experiments have revealed that shock waves in thermally relaxing gases, such as ionizing, dissociating and vibrationally excited gases, can become unstable. To date, the mechanism controlling this instability has not been resolved.…
An approach for quantitatively evaluating overshooting oscillations is designed to characterize the performance of shock-capturing schemes. Specifically, following our previous work focused on cases with only discontinuities, now we account…
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 provide a `user guide' to the literature of the past twenty years concerning the modeling and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit small-scale dependent shock waves. We cover several classes…
There are recent shifts in demand for design controllers from simplified to complex model-based. Although simplification approaches are successful in many areas of engineering control systems, high-fidelity simulation-based control design,…
The HLLEM scheme is a popular contact and shear preserving approximate Riemann solver for cheap and accurate computation of high speed gasdynamical flows. Unfortunately this scheme is known to be plagued by various forms of numerical shock…
A Lyapunov-based method is presented for stabilizing and controlling of closed quantum systems. The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite…
Shocks in granular media, such as vertically oscillated beds, have been shown to develop instabilities. Similar jet formation has been observed in explosively dispersed granular media. Our previous work addressed this instability by…
We construct a solution to a $2\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is…
We carry out the first rigorous numerical proof based on Evans function computations of stability of viscous shock profiles, for the system of isentropic gas dynamics with monatomic equation of state. We treat a selection of shock strengths…
High-speed turbulent flows are encountered in most space-related applications (including exploration, tourism and defense fields) and represent a subject of growing interest in the last decades. A major challenge in performing high-fidelity…
This paper extends our recent theoretical work concerning the feasibility of stable and accurate computation of turbulence using a large eddy simulation [Ida and Taniguchi, Phys. Rev. E 68, 036705 (2003)]. In our previous paper, it was…
In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools…