scholarly journals Explicit Large Time Stepping with Third-Order Exponential Time Differencing Scheme for Hypersonic Chemical Non-Equilibrium Flow

2018 ◽  
Vol 06 (01) ◽  
pp. 174-182
Author(s):  
Shiran Dai ◽  
Songping Wu
Keyword(s):  
Large Time ◽  
Equilibrium Flow ◽  
Third Order ◽  
Exponential Time ◽  
Exponential Time Differencing ◽  
Time Stepping ◽  
Non Equilibrium

Non-equilibrium flow over a wavy wall

1959 ◽  
Vol 6 (4) ◽  
pp. 481-496 ◽  
Author(s):  
Walter G. Vincenti
Keyword(s):  
Order Partial Differential Equation ◽  
Equilibrium Flow ◽  
Rate Parameter ◽  
Third Order ◽  
Pressure Drag ◽  
Inviscid Gas ◽  
Two Dimensional Flow ◽  
Flow Changes ◽  
Simple Fashion ◽  
Non Equilibrium

A small-disturbance solution is obtained for the steady two-dimensional flow over a sinusoidal wall of an inviscid gas in vibrational or chemical non-equilibrium. The results are based on a single, linear, third-order partial differential equation, which plays the same role here as does the Prandtl–Glauert equation in equilibrium flow. The solution is valid throughout the range from subsonic to supersonic speeds and for all values of the rate parameter from equilibrium to frozen flow (in both of which limits it reduces to Ackert's classical solution of the Prandtl–Glauert equation). The results illustrate in simple fashion some of the properties of non-equilibrium flow, such as the occurrence of pressure drag at subsonic speeds and the absence of the discontinuous phenomena that characterize the Prandtl–Glauert theory when the flow changes from subsonic to supersonic.

Numerical Solution of the Nonlinear Wave Equation via Fourth-Order Time Stepping

2015 ◽  
Vol 729 ◽  
pp. 213-219
Author(s):  
Mohammadreza Askaripour Lahiji ◽  
Zainal Abdul Aziz
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Fourth Order ◽  
Nonlinear Wave Equation ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Fisher Equation ◽  
Exponential Time ◽  
Exponential Time Differencing ◽  
Time Stepping

Some nonlinear wave equations are more difficult to solve analytically. Exponential Time Differencing (ETD) technique requires minimum stages to obtain the required accurateness, which suggests an efficient technique relating to computational duration that ensures remarkable stability characteristics upon resolving the nonlinear wave equations. This article solves the non-diagonal example of Fisher equation via the exponential time differencing Runge-Kutta 4 method (ETDRK4). Implementation of the method is demonstrated by short Matlab programs.

scholarly journals Exponential time differencing based efficient SC-PML for RCS simulation

2020 ◽  
Vol 31 (4) ◽  
pp. 703-711 ◽  
Author(s):  
Niu Liqiang ◽  
Xie Yongjun ◽  
Jiang Haolin ◽  
Wu Peiyu
Keyword(s):  
Exponential Time ◽  
Exponential Time Differencing

scholarly journals Exponential-time differencing schemes for low-mass DPD systems

2014 ◽  
Vol 185 (1) ◽  
pp. 229-235 ◽  
Author(s):  
N. Phan-Thien ◽  
N. Mai-Duy ◽  
D. Pan ◽  
B.C. Khoo
Keyword(s):  
Exponential Time ◽  
Exponential Time Differencing ◽  
Low Mass
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