Feedback control of monotonic shocks

5th International Conference on "Problems of Mathematical and Theoretical Physics and Mathematical Modelling"

物理学;数学

Porubov, A.V.^1,2,3 ; Bondarenkov, R.S.^2 ; Bouche, D.^4 ; Fradkov, A.L.^1,2

Institute of Problems in Mechanical Engineering, Bolshoy 61, V.O., Saint Petersburg

199178, Russia^1

St. Petersburg State Universitys, 7-9, Universitetskaya nab., V.O., Saint Petersburg

199034, Russia^2

St. Petersburg State Polytechnical University, Polytechnicheskaya st. 29, Saint Petersburg

195251, Russia^3

CMLA, ENS de Cachan, Cachan, France^4

关键词: High resolution scheme;    Monotonic shocks;    Nonlinear advection equation;    Second-order scheme;    Shock propagation;    Suppression of oscillations;    Switch-on;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/788/1/012030/pdf
DOI  :  10.1088/1742-6596/788/1/012030

来源: IOP

【 摘 要 】

The feedback control algorithm is developed to suppress oscillations caused by high resolution schemes. The stable propagation of the shock of the nonlinear advection equation is studied using the Lax-Wendroff and Warming- Beam second- order schemes. It is shown that the addition of one and the same control artificial term in both schemes results in efficient suppression of oscillations. The switch on/off the control is studied to demonstrate the role of the control in the stable monotonie shock propagation.