In this paper,we propose a spectral vanishing viscosity method for the triangular spectral element computation of high Reynolds number incompressible flows.This can be regarded as an extension of a similar stabilizati...In this paper,we propose a spectral vanishing viscosity method for the triangular spectral element computation of high Reynolds number incompressible flows.This can be regarded as an extension of a similar stabilization technique for the standard spectral element method.The difficulty of this extension lies in the fact that a suitable definition of spectral vanishing viscosity operator in non-structured elements does not exist,and it is not clear that if a suitably defined spectral vanishing viscosity provides desirable dissipation for the artificially accumulated energy.The main contribution of the paper includes:1)a well-defined spectral vanishing viscosity operator is proposed for non-standard spectral element methods for the Navier-Stokes equations based on triangular or tetrahedron partitions;2)an evaluation technique is introduced to efficiently implement the stabilization term without extra computational cost;3)the accuracy and efficiency of the proposed method is carefully examined through several numerical examples.Our numerical results show that the proposed method not only preserves the exponential convergence,but also produces improved accuracy when applied to the unsteady Navier-Stokes equations having smooth solutions.Especially,the stabilized triangular spectral element method efficiently stabilizes the simulation of high Reynolds incompressible flows.展开更多
An unstructured nodal spectral-elementmethod for theNavier-Stokes equations is developed in this paper.The method is based on a triangular and tetrahedral rational approximation and an easy-to-implement nodal basis wh...An unstructured nodal spectral-elementmethod for theNavier-Stokes equations is developed in this paper.The method is based on a triangular and tetrahedral rational approximation and an easy-to-implement nodal basis which fully enjoys the tensorial product property.It allows arbitrary triangular and tetrahedralmesh,affording greater flexibility in handling complex domains while maintaining all essential features of the usual spectral-element method.The details of the implementation and some numerical examples are provided to validate the efficiency and flexibility of the proposed method.展开更多
基金NNW2018-ZT4A06 project and NSFC grant 11971408Lizhen Chen is partially supported by Grant U1930402.
文摘In this paper,we propose a spectral vanishing viscosity method for the triangular spectral element computation of high Reynolds number incompressible flows.This can be regarded as an extension of a similar stabilization technique for the standard spectral element method.The difficulty of this extension lies in the fact that a suitable definition of spectral vanishing viscosity operator in non-structured elements does not exist,and it is not clear that if a suitably defined spectral vanishing viscosity provides desirable dissipation for the artificially accumulated energy.The main contribution of the paper includes:1)a well-defined spectral vanishing viscosity operator is proposed for non-standard spectral element methods for the Navier-Stokes equations based on triangular or tetrahedron partitions;2)an evaluation technique is introduced to efficiently implement the stabilization term without extra computational cost;3)the accuracy and efficiency of the proposed method is carefully examined through several numerical examples.Our numerical results show that the proposed method not only preserves the exponential convergence,but also produces improved accuracy when applied to the unsteady Navier-Stokes equations having smooth solutions.Especially,the stabilized triangular spectral element method efficiently stabilizes the simulation of high Reynolds incompressible flows.
基金The work of the second author is partially supported by NFS grant DMS-0610646The research of the third author was partially supported by National NSF of China(Grant number 11071203).
文摘An unstructured nodal spectral-elementmethod for theNavier-Stokes equations is developed in this paper.The method is based on a triangular and tetrahedral rational approximation and an easy-to-implement nodal basis which fully enjoys the tensorial product property.It allows arbitrary triangular and tetrahedralmesh,affording greater flexibility in handling complex domains while maintaining all essential features of the usual spectral-element method.The details of the implementation and some numerical examples are provided to validate the efficiency and flexibility of the proposed method.
