Uniformly high-order accurate non-oscillatory schemes, 1

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell

Some physical implications of recent solar wind measurements

The physical implications of the existence at about 1 AU of a quiet solar wind particle flux about 90 percent larger than that suggested in the past is investigated within the framework of the two-fluid solar wind model equations. During the spherically symmetric radial expansion of the quiet solar wind, the particle flux is conserved quantity. It is found that a pure collisional two-fluid model provides good particle density and streaming velocity at 1 AU, but predicts too large an electron temperature and too small a proton temperature. When noncollisional contributions to the transport coefficients are incorporated in the model equations, a complete satisfactory agreement with the available observations is obtained. Upper limits to the effective coupling between electrons and protons, as well as to the effective proton thermal conductivity, and both upper and lower limits to the effective electron thermal conductivity in the quiet solar wind, required to provide agreement with observations, are given

On the application and extension of Harten's high resolution scheme

Extensions of a second order high resolution explicit method for the numerical computation of weak solutions of one dimensonal hyperbolic conservation laws are discussed. The main objectives were (1) to examine the shock resoluton of Harten's method for a two dimensional shock reflection problem, (2) to study the use of a high resolution scheme as a post-processor to an approximate steady state solution, and (3) to construct an implicit in the delta-form using Harten's scheme for the explicit operator and a simplified iteration matrix for the implicit operator

Reinforcement learning for Order Acceptance on a shared resource

Order acceptance (OA) is one of the main functions in business control. Basically, OA involves for each order a reject/accept decision. Always accepting an order when capacity is available could disable the system to accept more convenient orders in the future with opportunity losses as a consequence. Another important aspect is the availability of information to the decision-maker. We use the stochastic modeling approach, Markov decision theory and learning methods from artificial intelligence to find decision policies, even under uncertain information. Reinforcement learning (RL) is a quite new approach in OA. It is capable of learning both the decision policy and incomplete information, simultaneously. It is shown here that RL works well compared with heuristics. Finding good heuristics in a complex situation is a delicate art. It is demonstrated that a RL trained agent can be used to support the detection of good heuristics

On the Nonlinearity of Modern Shock-Capturing Schemes

The development is reviewed of shock capturing methods, paying special attention to the increasing nonlinearity in the design of numerical schemes. The nature is studies of this nonlinearity and its relation to upwind differencing is examined. This nonlinearity of the modern shock capturing methods is essential, in the sense that linear analysis is not justified and may lead to wrong conclusions. Examples to demonstrate this point are given

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme

Uniformly high order accurate essentially non-oscillatory schemes 3

In this paper (a third in a series) the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws are presented. Also presented is a hierarchy of high order accurate schemes which generalizes Godunov's scheme and its second order accurate MUSCL extension to arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear