Discretization error estimation for flow simulations using general hybrid grids

Abstract

A primary area of the author’s work with his students is outlined in the present article. It regards the estimation of the discretization error with mixed-element and adaptive meshes. Use of general hybrid meshes for computational flow simulations is of importance due to the complexity of both the geometry and the fields. The meshes can consist of a mix of hexahedra, prisms and tetrahedra with pyramids being transitional elements. The discretization error is a primary component of the numerical error in flow simulations. Primary factors affecting it are the local density of the mesh, as well as its “distortions”, namely the variation in local size and orientation (stretching, skewness), the shape of the individual elements (shear, twist), and the local change in their type (grid interfaces). Two distinct approaches have been followed in order to estimate and control the discretization error. The grid-based (“a priori”) approach assesses mesh quality from the analytic expression of the truncation error. The solution-based (“a posteriori”) approach monitors approximations of the variation of flow quantities (“sensors”). Those are then applied to guide adaptation of the grid to the simulated flow field

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