Optimization of one-parameter family of integration formulae for solving stiff chemical-kinetic ODEs

A fast and robust Jacobian-free time-integration method—called Minimum-error Adaptation of a Chemical-Kinetic ODE Solver (MACKS)—for solving stiff ODEs pertaining to chemical-kinetics is proposed herein. The MACKS formulation is based on optimization of the one-parameter family of integration formulae coupled with a dual time-stepping method to facilitate error minimization. The proposed method demonstrates higher accuracy compared to the method—Extended Robustness-enhanced numerical algorithm (ERENA)—previously proposed by the authors. Additionally, when this method is employed in homogeneous-ignition simulations, it facilitates realization of faster performance compared to CVODE.

Aerodynamic Simulation of Helicopter Based on Polyhedron Nested Grid Technology

In this paper, a computational fluid dynamics (CFD) simulation method based on the polyhedral nested grid is developed. By comparing the simulation and test results of the hovering flow field of the Caradonna–Tung rotor, the forward flight flow field of the AH-1G rotor, the interference flow field of the Robin rotor/fuselage, and the hovering and forward flight flow field of a coaxial rotor, it is proven that the method proposed in this paper can achieve high calculation accuracy under various working conditions. The dual time-stepping method is used for the transient simulation, and the Spalart–Allmaras (S-A) turbulence model, which is widely used in aviation, is adopted in the simulation.

Dual Time-Stepping Using Second Derivatives

We present a modified formulation of the dual time-stepping technique which makes use of two derivatives in pseudo-time. This new technique retains and improves the convergence properties to the stationary solution. When compared with the conventional dual time-stepping, the method with two derivatives reduces the stiffness of the problem and requires fewer iterations for full convergence to steady-state. In the current formulation, these positive effects require that an approximation of the square root of the spatial operator is available and inexpensive.