The paper examines computational schemes for calculating the gradient of fluid dynamic quantities using grids of various types.The Green–Gaussmethod and the least squares method(LSM)used to develop a hybrid gradient ...The paper examines computational schemes for calculating the gradient of fluid dynamic quantities using grids of various types.The Green–Gaussmethod and the least squares method(LSM)used to develop a hybrid gradient calculation scheme are considered.It is demonstrated that the accuracy of gradient calculations may vary depending on the geometry of the control volume:the Green–Gauss method exhibits lower errors for strongly elongated thin cells and cells with curved edges,while for cells with orthogonal edges,it is preferable to use LSM.In order to improve the accuracy of calculations on unstructured grids,a hybrid gradient calculation scheme is proposed.This scheme computes the gradient by summing values derived from both the Green–Gauss method and LSM,given the weight function that incorporates the geometry of the control volume.The paper presents a formula for the weight function,which determines the contribution of each method within the hybrid scheme.The developed scheme is applied to the problem of supersonic flow around a cylinder with a needle on two unstructured grids,namely truncated hexagons and tetrahedra.It is shown that the proposed hybrid scheme reduces the error in calculating the aerodynamic characteristics of a streamlined object.展开更多
基金support of the national project“Science and Universities”within the framework of the pro-gram of the Ministry of Science and Higher Education of the Russian Federation for the creation of laboratories for young scientists No.FSWE-2024-0001(scientific topic:“Development of numerical methods,models and algorithms for description of fluid flows under natural conditions and normal and critical operating conditions of industrial facilities using exa-and zetta-scale supercomputers”)the program for development of the world-class scientific center“Supersonic”in 2020-2025 with the financial support of the Ministry of Science and Higher Education of the Russian Federation(Agreement dated April 20,2022,No.075-15-2022-309).
文摘The paper examines computational schemes for calculating the gradient of fluid dynamic quantities using grids of various types.The Green–Gaussmethod and the least squares method(LSM)used to develop a hybrid gradient calculation scheme are considered.It is demonstrated that the accuracy of gradient calculations may vary depending on the geometry of the control volume:the Green–Gauss method exhibits lower errors for strongly elongated thin cells and cells with curved edges,while for cells with orthogonal edges,it is preferable to use LSM.In order to improve the accuracy of calculations on unstructured grids,a hybrid gradient calculation scheme is proposed.This scheme computes the gradient by summing values derived from both the Green–Gauss method and LSM,given the weight function that incorporates the geometry of the control volume.The paper presents a formula for the weight function,which determines the contribution of each method within the hybrid scheme.The developed scheme is applied to the problem of supersonic flow around a cylinder with a needle on two unstructured grids,namely truncated hexagons and tetrahedra.It is shown that the proposed hybrid scheme reduces the error in calculating the aerodynamic characteristics of a streamlined object.
