A unified gas kinetic scheme for transport and collision effects in plasma

In this study, the Vlasov-Poisson equation with or without collision term for plasma is solved by the unified gas kinetic scheme (UGKS). The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range interaction. The distribution function is discretized in discrete particle velocity space. After the Vlasov equation is integrated in finite volumes of physical space, the numerical flux across a cell interface and source term for particle acceleration are computed to update the distribution function at next time step. The flux is decided by Riemann problem and variation of distribution function in discrete particle velocity space is evaluated with central difference method. A electron-ion collision model is introduced in the Vlasov equation. This finite volume method for the UGKS couples the free transport and long-range interaction between particles. The electric field induced by charged particles is controlled by the Poisson's equation. In this paper, the Poisson's equation is solved using the Green's function for two dimensional plasma system subjected to the symmetry or periodic boundary conditions. Two numerical tests of the linear Landau damping and the Gaussian beam are carried out to validate the proposed method. The linear electron plasma wave damping is simulated based on electron-ion collision operator. Compared with previous methods, it is shown that the current method is able to obtain accurate results of the Vlasov-Poisson equation with a time step much larger than the particle collision time. Highly non-equilibrium and rarefied plasma flows, such as electron flows driven by electromagnetic field, can be simulated easily.Comment: 33 pages, 13 figure

Real-time Digital Simulation of Guitar Amplifiers as Audio Effects

Práce se zabývá číslicovou simulací kytarových zesilovačů, jakož to nelineárních analogových hudebních efektů, v reálném čase. Hlavním cílem práce je návrh algoritmů, které by umožnily simulaci složitých systémů v reálném čase. Tyto algoritmy jsou prevážně založeny na automatizované DK-metodě a aproximaci nelineárních funkcí. Kvalita navržených algoritmů je stanovana pomocí poslechových testů.The work deals with the real-time digital simulation of guitar amplifiers considered as nonlinear analog audio effects. The main aim is to design algorithms which are able to simulate complex systems in real-time. These algorithms are mainly based on the automated DK-method and the approximation of nonlinear functions. Quality of the designed algorithms is evaluated using listening tests.

Einstein equations in the null quasi-spherical gauge III: numerical algorithms

We describe numerical techniques used in the construction of our 4th order evolution for the full Einstein equations, and assess the accuracy of representative solutions. The code is based on a null gauge with a quasi-spherical radial coordinate, and simulates the interaction of a single black hole with gravitational radiation. Techniques used include spherical harmonic representations, convolution spline interpolation and filtering, and an RK4 "method of lines" evolution. For sample initial data of "intermediate" size (gravitational field with 19% of the black hole mass), the code is accurate to 1 part in 10^5, until null time z=55 when the coordinate condition breaks down.Comment: Latex, 38 pages, 29 figures (360Kb compressed

3-D inelastic analysis methods for hot section components. Volume 2: Advanced special functions models

This Annual Status Report presents the results of work performed during the third year of the 3-D Inelastic Analysis Methods for Hot Sections Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of computer codes that permit more accurate and efficient three-dimensional analyses of selected hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The computer codes embody a progression of mathematical models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components