Numerical Method of Characteristics for Three-Dimensional Supersonic Flows† †English translation edited by S. Neumark, R.A.E., Farnborough.

1968 ◽  
pp. 41-122 ◽  
Author(s):  
P.I. CHUSHKIN
Keyword(s):  
Numerical Method ◽  
English Translation ◽  
Method Of Characteristics ◽  
Three Dimensional ◽  
Supersonic Flows

The method of characteristics for the three-dimensional unsteady magnetofluid dynamics of a multi-component medium

1966 ◽  
Vol 25 (1) ◽  
pp. 17-41 ◽  
Author(s):  
Harry Sauerwein Sauerwein
Keyword(s):  
Fluid Dynamics ◽  
Numerical Method ◽  
Method Of Characteristics ◽  
Three Dimensional ◽  
Computation Time ◽  
Hyperbolic Partial Differential Equations ◽  
Recent Experience ◽  
Local Wave ◽  
Chemically Reacting ◽  
Unsteady Problems

A general numerical method of characteristics applicable to problems in magneto-fluid dynamics as well as ordinary fluid dynamics is described. The method can be applied to unsteady three-dimensional flows of chemically reacting, non-equilibrium, multi-component media. Dissipative phenomena must be neglected in order to make the governing equations of change hyperbolic, because the method can be applied only to quasi-linear, hyperbolic, partial differential equations. Practical restrictions on computation time usually require unsteady problems to be limited to cases with short transient times although theoretically the method applies to all unsteady flows. In steady flow the local velocity must be greater than the largest local wave speed. The characteristic and compatibility equations are derived for the most general case of magnetofluid dynamics. A new finite-difference network and its corresponding equations are developed similarly. Specialization of the general method to consider simpler problems is outlined. Preliminary numerical results of calculations using the method are presented. The practicality and feasibility of utilizing the general numerical method of characteristics on presently available, electronic digital computers is evaluated in the light of recent experience in calculating multi-dimensional flows with the method.

scholarly journals The time domain numerical method of three-dimensional conductors including radiation with lumped parameter circuit

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Souma Jinno ◽  
Shuji Kitora ◽  
Hiroshi Toki ◽  
Masayuki Abe
Keyword(s):  
Numerical Method ◽  
Time Domain ◽  
Maxwell Equations ◽  
Three Dimensional ◽  
New Formalism ◽  
Vector Potentials ◽  
Lumped Parameter ◽  
Radiation Theory ◽  
Stable Solutions ◽  
The Time Domain

AbstractWe formulate a numerical method on the transmission and radiation theory of three-dimensional conductors starting from the Maxwell equations in the time domain. We include the delay effect in the integral equations for the scalar and vector potentials rigorously, which is vital to obtain numerically stable solutions for transmission and radiation phenomena in conductors. We provide a formalism to connect the conductors to any passive lumped-parameter circuits. We show one example of numerical calculations, demonstrating that the new formalism provides stable solutions to the transmission and radiation phenomena.

scholarly journals A Fast Two-Dimensional Numerical Method for the Wake Simulation of a Vertical Axis Wind Turbine

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 49
Author(s):  
Zheng Yuan ◽  
Jin Jiang ◽  
Jun Zang ◽  
Qihu Sheng ◽  
Ke Sun ◽  
...  
Keyword(s):  
Velocity Distribution ◽  
Numerical Method ◽  
Three Dimensional ◽  
Particle Method ◽  
Vortex Method ◽  
Vertical Axis ◽  
Two Dimensional ◽  
Vertical Axis Wind Turbine ◽  
Wake Effect ◽  
Array Design

In the array design of the vertical axis wind turbines (VAWT), the wake effect of the upstream VAWT on the downstream VAWT needs to be considered. In order to simulate the velocity distribution of a VAWT wake rapidly, a new two-dimensional numerical method is proposed, which can make the array design easier and faster. In this new approach, the finite vortex method and vortex particle method are combined to simulate the generation and evolution of the vortex, respectively, the fast multipole method (FMM) is used to accelerate the calculation. Based on a characteristic of the VAWT wake, that is, the velocity distribution can be fitted into a power-law function, a new correction model is introduced to correct the three-dimensional effect of the VAWT wake. Finally, the simulation results can be approximated to the published experimental results in the first-order. As a new numerical method to simulate the complex VAWT wake, this paper proves the feasibility of the method and makes a preliminary validation. This method is not used to simulate the complex three-dimensional turbulent evolution but to simulate the velocity distribution quickly and relatively accurately, which meets the requirement for rapid simulation in the preliminary array design.

Sign in / Sign up

Export Citation Format

Share Document