Numerical Methods for Two-Fluid Dispersive Fast MHD Phenomena

2011 ◽  
Vol 10 (1) ◽  
pp. 183-215 ◽  
Author(s):  
Bhuvana Srinivasan ◽  
Ammar Hakim ◽  
Uri Shumlak
Keyword(s):  
Wave Propagation ◽  
Numerical Methods ◽  
Discontinuous Galerkin ◽  
Equation System ◽  
Source Terms ◽  
Phase Errors ◽  
Wave Propagation Method ◽  
Fluid Equations ◽  
Runge Kutta ◽  
Two Fluid

AbstractThe finite volume wave propagation method and the finite element Runge-Kutta discontinuous Galerkin (RKDG) method are studied for applications to balance laws describing plasma fluids. The plasma fluid equations explored are dispersive and not dissipative. The physical dispersion introduced through the source terms leads to the wide variety of plasma waves. The dispersive nature of the plasma fluid equations explored separates the work in this paper from previous publications. The linearized Euler equations with dispersive source terms are used as a model equation system to compare the wave propagation and RKDG methods. The numerical methods are then studied for applications of the full two-fluid plasma equations. The two-fluid equations describe the self-consistent evolution of electron and ion fluids in the presence of electromagnetic fields. It is found that the wave propagation method, when run at a CFL number of 1, is more accurate for equation systems that do not have disparate characteristic speeds. However, if the oscillation frequency is large compared to the frequency of information propagation, source splitting in the wave propagation method may cause phase errors. The Runge-Kutta discontinuous Galerkin method providesmore accurate results for problems near steady-state aswell as problems with disparate characteristic speeds when using higher spatial orders.

COMPUTATIONAL ASPECTS OF THE DISCONTINUOUS GALERKIN METHOD FOR THE WAVE EQUATION

2008 ◽  
Vol 16 (04) ◽  
pp. 507-530 ◽  
Author(s):  
TIMO LÄHIVAARA ◽  
MATTI MALINEN ◽  
JARI P. KAIPIO ◽  
TOMI HUTTUNEN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Wave Equation ◽  
Discontinuous Galerkin ◽  
Homogeneous Medium ◽  
Polynomial Degree ◽  
Dg Method ◽  
Runge Kutta ◽  
Element Method

The Discontinuous Galerkin (DG) method is a powerful tool for numerically simulating wave propagation problems. In this paper, the time-dependent wave equation is solved using the DG method for spatial discretization; and the Crank–Nicolson and fourth-order explicit, singly diagonally implicit Runge–Kutta methods, and, for reference, the explicit Runge–Kutta method, were used for time integration. These simulation methods were studied using two-dimensional numerical experiments. The aim of the experiments was to study the effect of the polynomial degree of the basis functions, grid density, and the Courant–Friedrichs–Lewy number on the accuracy of the approximation. The sensitivity of the methods to distorted finite elements was also examined. Results from the DG method were compared with those computed using a conventional finite element method. Three different model problems were considered. In the first experiment, wave propagation in a homogeneous medium was studied. In the second experiment, the scattering and propagation of waves in an inhomogeneous medium were investigated. The third experiment evaluated wave propagation in a more complicated domain involving multiple scattering waves. The results indicated that the DG method provides more accurate solutions than the conventional finite element method with a reduced computation time and a lower number of degrees of freedom.

Optimization of the Navy’s three-dimensional mine impact burial prediction simulation model, Impact35, using high-order numerical methods

2021 ◽  
pp. 154851292110286
Author(s):  
Athanasios Donas ◽  
Ioannis Famelis ◽  
Peter C Chu ◽  
George Galanis
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Prediction Model ◽  
Simulation Model ◽  
Three Dimensional ◽  
Simulation System ◽  
High Order ◽  
Alternative Methodology ◽  
Runge Kutta ◽  
Fifth Order

The aim of this paper is to present an application of high-order numerical analysis methods to a simulation system that models the movement of a cylindrical-shaped object (mine, projectile, etc.) in a marine environment and in general in fluids with important applications in Naval operations. More specifically, an alternative methodology is proposed for the dynamics of the Navy’s three-dimensional mine impact burial prediction model, Impact35/vortex, based on the Dormand–Prince Runge–Kutta fifth-order and the singly diagonally implicit Runge–Kutta fifth-order methods. The main aim is to improve the time efficiency of the system, while keeping the deviation levels of the final results, derived from the standard and the proposed methodology, low.

Building Stiffness Estimation by Wave Traveling Times

2014 ◽  
Author(s):  
Jesús Morales-Valdez ◽  
Luis Alvarez-Icaza
Keyword(s):  
Wave Propagation ◽  
Modal Analysis ◽  
Single Layer ◽  
Original Formulation ◽  
Arrival Times ◽  
Identification Methods ◽  
Novel Technique ◽  
Wave Propagation Method ◽  
Local Technique ◽  
Interesting Alternative

A novel technique to estimate stiffness in buildings is presented. In contrast with most of the available work in the literature that resorts to diverse forms of modal analysis, this local technique is based on the propagation of a Ricker pulse through the structure and on measuring the wave arrival times at each story of the building, represented as a single layer in a multiple stratum model. These arrival times are later used to recuperate building stiffness at each story. Wave propagation is based on the Thomson-Haskell method, that allows to generalize the wave propagation method to multi-story buildings without significant changes to the original formulation. The number of calculated parameters is small in comparison with methods based on modal analysis. This technique provides and quick and easy methodology to assess building integrity and is an interesting alternative to verify results obtained by other identification methods. Simulation results for building with heterogeneous characteristics across the stories confirm the feasibility of the proposal.

Wave propagation in the presence of a spatially uniform external periodic magnetic field in two-temperature plasma

1982 ◽  
Vol 28 (1) ◽  
pp. 93-101
Author(s):  
Sanjay Kumar Ghosh
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Fluid Model ◽  
Hydrodynamic Equations ◽  
Temperature Plasma ◽  
Uniform External Magnetic Field ◽  
Two Fluid Model ◽  
Excitation Conditions ◽  
Two Fluid ◽  
Two Temperature

Starting from the two-fluid model hydrodynamic equations, a dispersion relation is obtained for wave propagation through a two-temperature plasma perpendicular to the direction of the spatially uniform external magnetic field B0cosω0t and several excitation conditions are deduced.

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