scholarly journals Positivity-preserving adaptive Runge–Kutta methods

2021 ◽  
Vol 16 (2) ◽  
pp. 155-179
Author(s):  
Stephan Nüßlein ◽  
Hendrik Ranocha ◽  
David I. Ketcheson
Keyword(s):  
Positivity Preserving ◽  
Runge Kutta

scholarly journals Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock

2016 ◽  
Vol 9 (1) ◽  
pp. 87-110 ◽  
Author(s):  
Jianming Liu ◽  
Jianxian Qiu ◽  
Mikhail Goman ◽  
Xinkai Li ◽  
Meilin Liu
Keyword(s):  
Discontinuous Galerkin ◽  
Compressible Flows ◽  
Strong Shock ◽  
Interpolation Formula ◽  
Cartesian Grid ◽  
Immersed Boundary ◽  
Positivity Preserving ◽  
Element Space ◽  
Runge Kutta ◽  
Adaptive Cartesian Grid

AbstractIn order to suppress the failure of preserving positivity of density or pressure, a positivity-preserving limiter technique coupled withh-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method is developed in this paper. Such a method is implemented to simulate flows with the large Mach number, strong shock/obstacle interactions and shock diffractions. The Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is also presented. This approach directly uses the cell solution polynomial of DG finite element space as the interpolation formula. The method is validated by the well documented test examples involving unsteady compressible flows through complex bodies over a large Mach numbers. The numerical results demonstrate the robustness and the versatility of the proposed approach.

A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye model

2017 ◽  
Vol 27 (03) ◽  
pp. 549-579 ◽  
Author(s):  
Juntao Huang ◽  
Chi-Wang Shu
Keyword(s):  
Discontinuous Galerkin ◽  
Strong Stability ◽  
Debye Model ◽  
Second Order ◽  
Positivity Preserving ◽  
Asymptotic Preserving ◽  
Runge Kutta ◽  
Numer Anal ◽  
Scalar Conservation ◽  
Unconditional Positivity

In this paper, we develop a second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin (DG) scheme for the Kerr–Debye model. By using the approach first introduced by Zhang and Shu in [Q. Zhang and C.-W. Shu, Error estimates to smooth solutions of Runge–Kutta discontinuous Galerkin methods for scalar conservation laws, SIAM J. Numer. Anal. 42 (2004) 641–666.] with an energy estimate and Taylor expansion, the asymptotic-preserving property of the semi-discrete DG methods is proved rigorously. In addition, we propose a class of unconditional positivity-preserving implicit–explicit (IMEX) Runge–Kutta methods for the system of ordinary differential equations arising from the semi-discretization of the Kerr–Debye model. The new IMEX Runge–Kutta methods are based on the modification of the strong-stability-preserving (SSP) implicit Runge–Kutta method and have second-order accuracy. The numerical results validate our analysis.

Semi-implicit Runge-Kutta schemes for stiff multi-dimensional reacting flows

1997 ◽  
Author(s):  
Jack Yoh ◽  
Xiaolin Zhong ◽  
Jack Yoh ◽  
Xiaolin Zhong
Keyword(s):  
Reacting Flows ◽  
Runge Kutta

Modelación, Simulación y Control de Aerogeneradores con Generador de Inducción Doblemente Alimentado Utilizando Matlab

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
W. Vásquez ◽  
J. Játiva
Keyword(s):  
Runge Kutta

En este trabajo se presenta la modelación de los componentes aerodinámicos, mecánicos, eléctricos y de control del aerogenerador con generador de inducción doblemente alimentado (DFIG). La modelación es empleada para crear un programa en el software Matlab. Se utiliza el método de Runge Kutta de cuarto orden para solucionar las ecuaciones diferenciales existentes en la modelación. La estrategia de control del convertidor PWM bidireccional se base en la técnica de control vectorial que emplea marcos de referencia giratorios, la cual permite el control de las potencias activa y reactiva producidas por el DFIG. Se describe el proceso de inicialización del sistema aerogenerador con DFIG, para obtener las condiciones de estado estable antes de iniciar la simulación. Se analiza el comportamiento del aerogenerador con DFIG ante cambios de la velocidad del viento y fallas de corto circuito. Los resultados finales muestran que la potencia activa del DFIG varía de acuerdo al comportamiento de la velocidad del viento, mientras que la potencia reactiva permanece casi invariante. Los resultados obtenidos son comparados con los resultados del modelo del aerogenerador con DFIG existente en Simulink de Matlab.

Sign in / Sign up

Export Citation Format

Share Document