Study On Robustness And Convergence Of Separated Pressure-Based Algorithm

Computational fluid dynamics is increasingly playing an irreplaceable role in various fields.The application and research based on large open-source computational fluid dynamics plat-forms are an important option to achieve independence.In order to solve the numerical stabil-ity and convergence problems of PISO/SIMPLE algorithm in transient compressible flow,the robustness and convergence strategy of separated pressure based algorithm are studied in this paper.Firstly,the effects of prediction and correction on the robustness and convergence of the separated algorithm are discussed from the perspective of production and propagation of error,while the advantages and disadvantages of under-relaxation are reviewed from the perspec-tive of ensuring stability and promoting convergence.Based on the theoretical results above,an intelligent strategy for predictor and corrector according to the coupling degree of pressure and velocity is proposed,together with an under-relaxation scheme optimized according to the mathematical characteristics of the pressure—velocity correction and the non-orthogonal cor-rection,as well as the bounded linear scheme.The overall procedure is named as EPPL(Error Production and Propagation Limited).Tests of incompressible,transonic and supersonic flow show that EPPL not only has better robustness and efficiency,but also partially overcomes the convergence stagnation of the separated algorithm when compared with other algorithms.Secondly,in view of the problem that EPPL is still not robust enough in highly under-expanded jets,the effect of pressure-equation on accuracy and stability is analyzed.The deriva-tion proves that the pressure-equation has an additional error on the non-uniform grid when compared with the pressure-correction-equation,and analysis shows that the aliasing error in-troduced by inappropriate implicitization of density is the key factor leading to the divergence of pressure-equation for compressible flow.In addition,schemes based Crank-Nicolson’s method and pressure implicit relaxation to reduce the dissipation of Rhie-Chow interpolation are pro-posed for transient and steady-state flow,respectively,and a hybrid scheme for the calculation of mass-flux that account accuracy and stability is proposed for all-speed flow.Tests show that the improved EPPL algorithm not only has better accuracy and robustness,but also obtains the ability to simulate all-speed flow.Finally,in the engineering application of EPPL algorithm combined with KT/KNP scheme,the fully implicit and correction-based implicit KT/KNP scheme are presented,as well as the correction-based KT/KNP scheme for mass flux,and the second-order anti-diffusion term for unstructured grid is adopted.In addition,a Newton-like mass flux linearization scheme for separated algorithm is presented,and the solution procedure of EPPL is further optimized for adaptive mesh refinement,which alleviates the divergence caused by topology change and dy-namic load balancing.Tests show that the maximum time step of the implicit KT/KNP scheme is about 2 to 3 times that of the explicit one,and the comprehensive dynamic discontinuous cap-ture scheme achieves at least 5 times more efficiency improvement.And the comprehensive dynamic discontinuous capture scheme achieves at least more than 5 times efficiency improvement.