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...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%.展开更多
.Reductions of the self-consistent mean field theory model of amphiphilic molecules in solvent can lead to a singular family of functionalized Cahn-Hilliard(FCH)energies.We modify these energies,mollifying the singula....Reductions of the self-consistent mean field theory model of amphiphilic molecules in solvent can lead to a singular family of functionalized Cahn-Hilliard(FCH)energies.We modify these energies,mollifying the singularities to stabilize the computation of the gradient flows and develop a series of benchmark problems that emulate the“morphological complexity”observed in experiments.These benchmarks investigate the delicate balance between the rate of absorption of amphiphilic material onto an interface and a least energy mechanism to disperse the arriving mass.The result is a trichotomy of responses in which two-dimensional interfaces either lengthen by a regularized motion against curvature,undergo pearling bifurcations,or split directly into networks of interfaces.We evaluate a number of schemes that use second order backward differentiation formula(BDF2)type time stepping coupled with Fourier pseudo-spectral spatial discretization.The BDF2-type schemes are either based on a fully implicit time discretization with a preconditioned steepest descent(PSD)nonlinear solver or upon linearly implicit time discretization based on the standard implicitexplicit(IMEX)and the scalar auxiliary variable(SAV)approaches.We add an exponential time differencing(ETD)scheme for comparison purposes.All schemes use a fixed local truncation error target with adaptive time-stepping to achieve the error target.Each scheme requires proper“preconditioning”to achieve robust performance that can enhance efficiency by several orders of magnitude.The nonlinear PSD scheme achieves the smallest global discretization error at fixed local truncation error,however the IMEX and SAV schemes are the most computationally efficient as measured by the number of Fast Fourier Transform(FFT)calls required to achieve a desired global error.Indeed the performance of the SAV scheme directly mirrors that of IMEX,modulo a factor of 1.4 in FFT calls for the auxiliary variable system.展开更多
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 n...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.展开更多
基金support of the National Natural Science Foundation of China (No.52007002)the Science Center for Gas Turbine Project,China (No.P2022-A-II-007-001)the Fundamental Research Funds for the Central Universities,China (No.NS2023010).
文摘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%.
基金A.Christlieb acknowledges support from NSF grant DMS-1912183K.Promislow acknowledges support from NSF grant DMS-1813203 and DMS-2205553+2 种基金Z.Tan recognizes support from the China Scholarship Council under 201906160032B.Wetton recognizes support from a Canadian NSERC grantS.M.Wise recognizes support from NSF grants DMS-2012634 and DMS-2309547.
文摘.Reductions of the self-consistent mean field theory model of amphiphilic molecules in solvent can lead to a singular family of functionalized Cahn-Hilliard(FCH)energies.We modify these energies,mollifying the singularities to stabilize the computation of the gradient flows and develop a series of benchmark problems that emulate the“morphological complexity”observed in experiments.These benchmarks investigate the delicate balance between the rate of absorption of amphiphilic material onto an interface and a least energy mechanism to disperse the arriving mass.The result is a trichotomy of responses in which two-dimensional interfaces either lengthen by a regularized motion against curvature,undergo pearling bifurcations,or split directly into networks of interfaces.We evaluate a number of schemes that use second order backward differentiation formula(BDF2)type time stepping coupled with Fourier pseudo-spectral spatial discretization.The BDF2-type schemes are either based on a fully implicit time discretization with a preconditioned steepest descent(PSD)nonlinear solver or upon linearly implicit time discretization based on the standard implicitexplicit(IMEX)and the scalar auxiliary variable(SAV)approaches.We add an exponential time differencing(ETD)scheme for comparison purposes.All schemes use a fixed local truncation error target with adaptive time-stepping to achieve the error target.Each scheme requires proper“preconditioning”to achieve robust performance that can enhance efficiency by several orders of magnitude.The nonlinear PSD scheme achieves the smallest global discretization error at fixed local truncation error,however the IMEX and SAV schemes are the most computationally efficient as measured by the number of Fast Fourier Transform(FFT)calls required to achieve a desired global error.Indeed the performance of the SAV scheme directly mirrors that of IMEX,modulo a factor of 1.4 in FFT calls for the auxiliary variable system.
基金supported by the Hong Kong General Research Fund (Grant Nos. 202112, 15302214 and 509213)National Natural Science Foundation of China/Research Grants Council Joint Research Scheme (Grant Nos. N HKBU204/12 and 11261160486)+1 种基金National Natural Science Foundation of China (Grant No. 11471046)the Ministry of Education Program for New Century Excellent Talents Project (Grant No. NCET-12-0053)
文摘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.
