A new approach for reducing error of the volume penalization method is proposed.The mask function is modified by shifting the interface between solid and fluid by√νηtoward the fluid region,whereνandηare the visco...A new approach for reducing error of the volume penalization method is proposed.The mask function is modified by shifting the interface between solid and fluid by√νηtoward the fluid region,whereνandηare the viscosity and the permeability,respectively.The shift length√νηis derived from the analytical solution of the one-dimensional diffusion equation with a penalization term.The effect of the error reduction is verified numerically for the one-dimensional diffusion equation,Burgers’equation,and the two-dimensional Navier-Stokes equations.The results show that the numerical error is reduced except in the vicinity of the interface showing overall second-order accuracy,while it converges to a non-zero constant value as the number of grid points increases for the original mask function.However,the new approach is effective when the grid resolution is sufficiently high so that the boundary layer,whose width is proportional to√νη,is resolved.Hence,the approach should be used when an appropriate combination ofνandηis chosen with a given numerical grid.展开更多
The sophisticated structures of flapping insect wings make it challenging to study the role of wing flexibility in insect flight.In this study,a mass-spring system is used to model wing structural dynamics as a thin,f...The sophisticated structures of flapping insect wings make it challenging to study the role of wing flexibility in insect flight.In this study,a mass-spring system is used to model wing structural dynamics as a thin,flexible membrane supported by a network of veins.The vein mechanical properties can be estimated based on their diameters and the Young's modulus of cuticle.In order to analyze the effect of wing flexibility,the Young's modulus is varied to make a comparison between two different wing models that we refer to as flexible and highly flexible.The wing models are coupled with a pseudo-spectral code solving the incompressible Navier–Stokes equations,allowing us to investigate the influence of wing deformation on the aerodynamic efficiency of a tethered flapping bumblebee.Compared to the bumblebee model with rigid wings,the one with flexible wings flies more efficiently,characterized by a larger lift-to-power ratio.展开更多
文摘A new approach for reducing error of the volume penalization method is proposed.The mask function is modified by shifting the interface between solid and fluid by√νηtoward the fluid region,whereνandηare the viscosity and the permeability,respectively.The shift length√νηis derived from the analytical solution of the one-dimensional diffusion equation with a penalization term.The effect of the error reduction is verified numerically for the one-dimensional diffusion equation,Burgers’equation,and the two-dimensional Navier-Stokes equations.The results show that the numerical error is reduced except in the vicinity of the interface showing overall second-order accuracy,while it converges to a non-zero constant value as the number of grid points increases for the original mask function.However,the new approach is effective when the grid resolution is sufficiently high so that the boundary layer,whose width is proportional to√νη,is resolved.Hence,the approach should be used when an appropriate combination ofνandηis chosen with a given numerical grid.
基金Financial support from the Agence Nationale de la Recherche(ANR)(Grant 15-CE40-0019)and Deutsche Forschungsgemeinschaft(DFG)(Grant SE 824/26-1),project AIFITHPC resources of IDRIS under the allocation No.2018-91664 attributed by Grand Equipement National de Calcul Intensif(GENCI)+2 种基金Centre de Calcul Intensif d'Aix-Marseille is acknowledged for granting access to its high performance computing resources financed by the project Equip@Meso(No.ANR-10-EQPX-29-01)financial support granted by the ministeres des Affaires etrangeres et du developpement international(MAEDI)et de l'Education nationale et l'enseignement superieur,de la recherche et de l'innovation(MENESRI),the Deutscher Akademischer Austauschdienst(DAAD)within the French-German Procope project FIFITfinancial support from the JSPS KAKENHI Grant No.JP18K13693。
文摘The sophisticated structures of flapping insect wings make it challenging to study the role of wing flexibility in insect flight.In this study,a mass-spring system is used to model wing structural dynamics as a thin,flexible membrane supported by a network of veins.The vein mechanical properties can be estimated based on their diameters and the Young's modulus of cuticle.In order to analyze the effect of wing flexibility,the Young's modulus is varied to make a comparison between two different wing models that we refer to as flexible and highly flexible.The wing models are coupled with a pseudo-spectral code solving the incompressible Navier–Stokes equations,allowing us to investigate the influence of wing deformation on the aerodynamic efficiency of a tethered flapping bumblebee.Compared to the bumblebee model with rigid wings,the one with flexible wings flies more efficiently,characterized by a larger lift-to-power ratio.
