As a new type of hull form,trimaran has remarkable excellent performances and has drawn more and more attention.When the viscous CFD technology now available is applied to the research of resistance performance of tri...As a new type of hull form,trimaran has remarkable excellent performances and has drawn more and more attention.When the viscous CFD technology now available is applied to the research of resistance performance of trimaran,the spatial discretization would usually result in the grid error and uncertainty,and thus the considerable discrepancy between the numerical results and the experimental data.In order to ascertain how much the grid would affect the calculation,the grid convergence should be studied.A mathematical trimaran was chosen as an example,with the commercial code CFX for the simulation,VOF for surface treatment,and the grid study was carried out based on two different turbulence models.It was concluded that carrying out grid study is helpful in estimating the grid error and uncertainty,and indicating the direction of improving the credibility of the numerical calculation, and,in addition to grid errors and uncertainties,the turbulence modeling errors and uncertainties contribute to the simulation errors.展开更多
The accuracy of gradient reconstruction methods on unstructured meshes is analyzed both mathematically and numerically.Mathematical derivations reveal that,for gradient reconstruction based on the Green-Gauss theorem(...The accuracy of gradient reconstruction methods on unstructured meshes is analyzed both mathematically and numerically.Mathematical derivations reveal that,for gradient reconstruction based on the Green-Gauss theorem(the GG methods),if the summation of first-and-lower-order terms does not counterbalance in the discretized integral process,which rarely occurs,second-order accurate approximation of face midpoint value is necessary to produce at least first-order accurate gradient.However,gradient reconstruction based on the least-squares approach(the LSQ methods)is at least first-order on arbitrary unstructured grids.Verifications are performed on typical isotropic grid stencils by analyzing the relationship between the discretization error of gradient reconstruction and the discretization error of the face midpoint value approximation of a given analytic function.Meanwhile,the numerical accuracy of gradient reconstruction methods is examined with grid convergence study on typical isotropic grids.Results verify the phenomenon of accuracy degradation for the GG methods when the face midpoint value condition is not satisfied.The LSQ methods are proved to be at least first-order on all tested isotropic grids.To study gradient accuracy effects on inviscid flow simulation,solution errors are quantified using the Method of Manufactured Solutions(MMS)which was validated before adoption by comparing with an exact solution case,i.e.,the 2-dimensional(2D)inviscid isentropic vortex.Numerical results demonstrate that the order of accuracy(OOA)of gradient reconstruction is crucial in determining the OOA of numerical solutions.Solution accuracy deteriorates seriously if gradient reconstruction does not reach first-order.展开更多
文摘As a new type of hull form,trimaran has remarkable excellent performances and has drawn more and more attention.When the viscous CFD technology now available is applied to the research of resistance performance of trimaran,the spatial discretization would usually result in the grid error and uncertainty,and thus the considerable discrepancy between the numerical results and the experimental data.In order to ascertain how much the grid would affect the calculation,the grid convergence should be studied.A mathematical trimaran was chosen as an example,with the commercial code CFX for the simulation,VOF for surface treatment,and the grid study was carried out based on two different turbulence models.It was concluded that carrying out grid study is helpful in estimating the grid error and uncertainty,and indicating the direction of improving the credibility of the numerical calculation, and,in addition to grid errors and uncertainties,the turbulence modeling errors and uncertainties contribute to the simulation errors.
基金National Natural Science Foundation of China[grant numbers 11532016,91530325].
文摘The accuracy of gradient reconstruction methods on unstructured meshes is analyzed both mathematically and numerically.Mathematical derivations reveal that,for gradient reconstruction based on the Green-Gauss theorem(the GG methods),if the summation of first-and-lower-order terms does not counterbalance in the discretized integral process,which rarely occurs,second-order accurate approximation of face midpoint value is necessary to produce at least first-order accurate gradient.However,gradient reconstruction based on the least-squares approach(the LSQ methods)is at least first-order on arbitrary unstructured grids.Verifications are performed on typical isotropic grid stencils by analyzing the relationship between the discretization error of gradient reconstruction and the discretization error of the face midpoint value approximation of a given analytic function.Meanwhile,the numerical accuracy of gradient reconstruction methods is examined with grid convergence study on typical isotropic grids.Results verify the phenomenon of accuracy degradation for the GG methods when the face midpoint value condition is not satisfied.The LSQ methods are proved to be at least first-order on all tested isotropic grids.To study gradient accuracy effects on inviscid flow simulation,solution errors are quantified using the Method of Manufactured Solutions(MMS)which was validated before adoption by comparing with an exact solution case,i.e.,the 2-dimensional(2D)inviscid isentropic vortex.Numerical results demonstrate that the order of accuracy(OOA)of gradient reconstruction is crucial in determining the OOA of numerical solutions.Solution accuracy deteriorates seriously if gradient reconstruction does not reach first-order.
