For a complex flow about multi-element airfoils a mixed grid method is set up. C-type grids are produced on each element′s body and in their wakes at first, O-type grids are given in the outmost area, and H-type grid...For a complex flow about multi-element airfoils a mixed grid method is set up. C-type grids are produced on each element′s body and in their wakes at first, O-type grids are given in the outmost area, and H-type grids are used in middle additional areas. An algebra method is used to produce the initial grids in each area. And the girds are optimized by elliptical differential equation method. Then C-O-H zonal patched grids around multi-element airfoils are produced automatically and efficiently. A time accurate finite-volume integration method is used to solve the compressible laminar and turbulent Navier-Stokes (N-S) equations on the grids. Computational results prove the method to be effective.展开更多
In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),...In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),the Laplacian discretisation is often required in order to solve the governing equations and/or estimate physical quantities(such as the viscous stresses).In some meshless applications,the Laplacians are also needed as stabilisation operators to enhance the pressure calculation.The particles in the Lagrangian methods move following the material velocity,yielding a disordered(random)particle distribution even though they may be distributed uniformly in the initial state.Different schemes have been developed for a direct estimation of second derivatives using finite difference,kernel integrations and weighted/moving least square method.Some of the schemes suffer from a poor convergent rate.Some have a better convergent rate but require inversions of high order matrices,yielding high computational costs.This paper presents a quadric semi-analytical finite-difference interpolation(QSFDI)scheme,which can achieve the same degree of the convergent rate as the best schemes available to date but requires the inversion of significant lower-order matrices,i.e.3×3 for 3D cases,compared with 6×6 or 10×10 in the schemes with the best convergent rate.Systematic patch tests have been carried out for either estimating the Laplacian of given functions or solving Poisson’s equations.The convergence,accuracy and robustness of the present schemes are compared with the existing schemes.It will show that the present scheme requires considerably less computational time to achieve the same accuracy as the best schemes available in literatures,particularly for estimating the Laplacian of given functions.展开更多
强耦合条件下,复杂系统的有限元分析受到自由度的影响计算成本高昂。虽然模态叠加技术能减少耦合系统的自由度,但基于忽略不同子系统间高阶模态和低阶模态耦合作用的假设,若使用非耦合模态可能导致收敛性差。基于无阻尼声振耦合方程,本...强耦合条件下,复杂系统的有限元分析受到自由度的影响计算成本高昂。虽然模态叠加技术能减少耦合系统的自由度,但基于忽略不同子系统间高阶模态和低阶模态耦合作用的假设,若使用非耦合模态可能导致收敛性差。基于无阻尼声振耦合方程,本文采用分片传递函数法(Patch transfer function method,PTFM)将耦合面处理成一系列独立的分片,每个分片上所属单元节点值的平均值定义为分片传递函数,通过使用连续性关系计算耦合系统的分片传递函数。将耦合矩阵的求逆简化为源点到响应点的传递函数,可以快速计算耦合系统响应值。分别利用直接耦合法(Direct coupling method,DCM)和分片传递函数法计算板和空气声腔耦合模型,验证分片传递函数法的有效性,并讨论了分片传递函数的算法原理和计算误差。展开更多
文摘For a complex flow about multi-element airfoils a mixed grid method is set up. C-type grids are produced on each element′s body and in their wakes at first, O-type grids are given in the outmost area, and H-type grids are used in middle additional areas. An algebra method is used to produce the initial grids in each area. And the girds are optimized by elliptical differential equation method. Then C-O-H zonal patched grids around multi-element airfoils are produced automatically and efficiently. A time accurate finite-volume integration method is used to solve the compressible laminar and turbulent Navier-Stokes (N-S) equations on the grids. Computational results prove the method to be effective.
文摘In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),the Laplacian discretisation is often required in order to solve the governing equations and/or estimate physical quantities(such as the viscous stresses).In some meshless applications,the Laplacians are also needed as stabilisation operators to enhance the pressure calculation.The particles in the Lagrangian methods move following the material velocity,yielding a disordered(random)particle distribution even though they may be distributed uniformly in the initial state.Different schemes have been developed for a direct estimation of second derivatives using finite difference,kernel integrations and weighted/moving least square method.Some of the schemes suffer from a poor convergent rate.Some have a better convergent rate but require inversions of high order matrices,yielding high computational costs.This paper presents a quadric semi-analytical finite-difference interpolation(QSFDI)scheme,which can achieve the same degree of the convergent rate as the best schemes available to date but requires the inversion of significant lower-order matrices,i.e.3×3 for 3D cases,compared with 6×6 or 10×10 in the schemes with the best convergent rate.Systematic patch tests have been carried out for either estimating the Laplacian of given functions or solving Poisson’s equations.The convergence,accuracy and robustness of the present schemes are compared with the existing schemes.It will show that the present scheme requires considerably less computational time to achieve the same accuracy as the best schemes available in literatures,particularly for estimating the Laplacian of given functions.
文摘强耦合条件下,复杂系统的有限元分析受到自由度的影响计算成本高昂。虽然模态叠加技术能减少耦合系统的自由度,但基于忽略不同子系统间高阶模态和低阶模态耦合作用的假设,若使用非耦合模态可能导致收敛性差。基于无阻尼声振耦合方程,本文采用分片传递函数法(Patch transfer function method,PTFM)将耦合面处理成一系列独立的分片,每个分片上所属单元节点值的平均值定义为分片传递函数,通过使用连续性关系计算耦合系统的分片传递函数。将耦合矩阵的求逆简化为源点到响应点的传递函数,可以快速计算耦合系统响应值。分别利用直接耦合法(Direct coupling method,DCM)和分片传递函数法计算板和空气声腔耦合模型,验证分片传递函数法的有效性,并讨论了分片传递函数的算法原理和计算误差。
