This paper analyzes a time variable filter approach for the nonlinear fluidfluid interaction problem.The method applies a time variable filter to improve numerical solution of a variable time step Euler scheme with ex...This paper analyzes a time variable filter approach for the nonlinear fluidfluid interaction problem.The method applies a time variable filter to improve numerical solution of a variable time step Euler scheme with explicit second-order extrapolation treatment for nonlinear convection and interface terms.Compared with classical second-order method in time,the proposed approach improves time accuracy from the first order to the second order by adding several lines to the code of variable time step Euler scheme.Theoretically,we prove the unconditional energy stability,local H^(1) stability and error estimates.Numerically,some numerical experiments are provided to test the theoretical results,which illustrate the accuracy and efficiency of the presented method.展开更多
In this paper,a fully discrete finite element scheme with second-order temporal accuracy is proposed for a fluid-fluid interaction model,which consists of two Navier-Stokes equations coupled by a linear interface cond...In this paper,a fully discrete finite element scheme with second-order temporal accuracy is proposed for a fluid-fluid interaction model,which consists of two Navier-Stokes equations coupled by a linear interface condition.The proposed fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization,the secondorder backward differentiation formula for temporal discretization,the second-order Gear’s extrapolation approach for the interface terms and extrapolated treatments in linearization for the nonlinear terms.Moreover,the unconditional stability is established by rigorous analysis and error estimate for the fully discrete scheme is also derived.Finally,some numerical experiments are carried out to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme.展开更多
This paper investigates two methods of coupling fluids across an interface,motivated by air-sea interaction in application codes.One method is for sequential configurations,where the air code module in invoked over so...This paper investigates two methods of coupling fluids across an interface,motivated by air-sea interaction in application codes.One method is for sequential configurations,where the air code module in invoked over some time interval prior to the sea module.The other method is for concurrent setups,in which the air and sea modules run in parallel.The focus is the temporal representation of air-sea fluxes.The methods we study conserve moments of the fluxes,with an arbitrary order of accuracy possible in time.Different step sizes are allowed for the two fluid codes.An a posteriori stability indicator is defined,which can be computed efficiently on-the-fly over each coupling interval.For a model of two coupled fluids with natural heat convection,using finite elements in space,we prove the sufficiency of our stability indicator.Under certain conditions,we also prove that stability can be enforced by iteration when the coupling interval is small enough.In particular,for solutions in a certain class,we show that the step size scaling is no worse than O(h)in three dimensions of space,where Oh is a mesh parameter.This is a sharper result than what has been shown previously for related algorithms with finite element methods.Computational examples illustrate the behavior of the algorithms under a wide variety of configurations.展开更多
基金supported by the Natural Science Foundation of China(grant number 12361077)Natural Science Foundation of Xinjiang Uygur Autonomous Region(grant number 2023D14014).
文摘This paper analyzes a time variable filter approach for the nonlinear fluidfluid interaction problem.The method applies a time variable filter to improve numerical solution of a variable time step Euler scheme with explicit second-order extrapolation treatment for nonlinear convection and interface terms.Compared with classical second-order method in time,the proposed approach improves time accuracy from the first order to the second order by adding several lines to the code of variable time step Euler scheme.Theoretically,we prove the unconditional energy stability,local H^(1) stability and error estimates.Numerically,some numerical experiments are provided to test the theoretical results,which illustrate the accuracy and efficiency of the presented method.
基金supported by the Natural Science Foundation of China(grant numbers 11861067 and 11771348)Natural Science Foundation of Xinjiang Province(grant number 2021D01E11).
文摘In this paper,a fully discrete finite element scheme with second-order temporal accuracy is proposed for a fluid-fluid interaction model,which consists of two Navier-Stokes equations coupled by a linear interface condition.The proposed fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization,the secondorder backward differentiation formula for temporal discretization,the second-order Gear’s extrapolation approach for the interface terms and extrapolated treatments in linearization for the nonlinear terms.Moreover,the unconditional stability is established by rigorous analysis and error estimate for the fully discrete scheme is also derived.Finally,some numerical experiments are carried out to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme.
文摘This paper investigates two methods of coupling fluids across an interface,motivated by air-sea interaction in application codes.One method is for sequential configurations,where the air code module in invoked over some time interval prior to the sea module.The other method is for concurrent setups,in which the air and sea modules run in parallel.The focus is the temporal representation of air-sea fluxes.The methods we study conserve moments of the fluxes,with an arbitrary order of accuracy possible in time.Different step sizes are allowed for the two fluid codes.An a posteriori stability indicator is defined,which can be computed efficiently on-the-fly over each coupling interval.For a model of two coupled fluids with natural heat convection,using finite elements in space,we prove the sufficiency of our stability indicator.Under certain conditions,we also prove that stability can be enforced by iteration when the coupling interval is small enough.In particular,for solutions in a certain class,we show that the step size scaling is no worse than O(h)in three dimensions of space,where Oh is a mesh parameter.This is a sharper result than what has been shown previously for related algorithms with finite element methods.Computational examples illustrate the behavior of the algorithms under a wide variety of configurations.
