In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary varia...In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.展开更多
In this article,the global attractors of 2D g-Navier-Stokes equations are obtained in the space of C_(Hg) and CVg respectively.When the external force f is sufficiently small,the studies indicate that the global attra...In this article,the global attractors of 2D g-Navier-Stokes equations are obtained in the space of C_(Hg) and CVg respectively.When the external force f is sufficiently small,the studies indicate that the global attractor in C_(Hg) is equal to the global attractor in C_(Vg).展开更多
Cauchy problem for the linearized bipolar isentropic Navier-Stokes-Poisson system in R^(2) is studied.Through the reformulation of unknown functions,we change the formal system into a linearized Navier-Stokes system a...Cauchy problem for the linearized bipolar isentropic Navier-Stokes-Poisson system in R^(2) is studied.Through the reformulation of unknown functions,we change the formal system into a linearized Navier-Stokes system and a unipolar Navier-Stokes-Poisson system.Based on a delicate analysis of the corresponding Green function,L^(2) decay estimate of the solution is obtained.展开更多
基金Supported by the Research Project Supported of Shanxi Scholarship Council of China(No.2021-029)Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)Shanxi Province Natural Science Research(202203021211129)。
文摘In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.
基金Supported by the National Natural Science Foundation of China(11971378)Shaanxi Fundamental Science Research Project for Mathematics and Physics(23JSY050)Shaanxi Innovative Training Program for College Students(S202410719114)。
文摘In this article,the global attractors of 2D g-Navier-Stokes equations are obtained in the space of C_(Hg) and CVg respectively.When the external force f is sufficiently small,the studies indicate that the global attractor in C_(Hg) is equal to the global attractor in C_(Vg).
基金Supported by the National Natural Science Foundation of China (12271141)。
文摘Cauchy problem for the linearized bipolar isentropic Navier-Stokes-Poisson system in R^(2) is studied.Through the reformulation of unknown functions,we change the formal system into a linearized Navier-Stokes system and a unipolar Navier-Stokes-Poisson system.Based on a delicate analysis of the corresponding Green function,L^(2) decay estimate of the solution is obtained.
