An optimized time-adaptive aerothermal coupling calculation method for aerothermal analysis of disc cavity system

In order to further achieve the balance between the calculation accuracy and efficiency of the transient analysis of the aero-engine disc cavity system,an Optimized Time-adaptive Aerother-mal Coupling calculation(OTAC)method has been proposed.It combines one-dimensional tran-sient calculation of air system,Conventional Sequence Staggered(CSS)method,Time-adaptive Aerothermal Coupling calculation(TAC)method and differential evolution optimization algorithm to obtain an efficient and high-precision aerothermal coupling calculation method of air system.Considering both the heat conduction in the solid domain and the flow in the fluid domain as unsteady states in the OTAC,the interaction of fluid-solid information within a single coupling time step size was implemented based on the CSS method.Furthermore,the coupling time step size was automatically adjusted with the number of iterations by using the Proportional-Integral-Deri vative(PID)controller.Results show that when compared with the traditional loosely coupling method with a fixed time step size,the computational accuracy and efficiency of the OTAC method are improved by 8.9%and 30%,respectively.Compared with the tight coupling calculation,the OTAC method can achieve a speedup of 1 to 2 orders of magnitude,while the calculation error is maintained within 6.1%.

An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.