An efficient, high-order, conservative method named the spectral difference method has been developed recently for conservation laws on unstructured grids. It combines the best features of structured and unstructured grid methods to achieve high-computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. The method is easy to implement since it does not involve surface or volume integrals. Universal reconstructions are obtained by distributing solution and flux points in a geometrically similar manner for simplex cells. In this paper, the method is further extended to nonlinear systems of conservation laws, the Euler equations. Accuracy studies are performed to numerically verify the order of accuracy. In order to capture both smooth feature and discontinuities, monotonicity limiters are implemented, and tested for several problems in one and two dimensions. The method is more efficient than the discontinuous Galerkin and spectral volume methods for unstructured grids.
We present a comparison between hybridized and non-hybridized discontinuous Galerkin methods in the context of target-based hp-adaptation. Using a discrete-adjoint approach, sensitivities with respect to output functionals are computed to drive the adaptation. From the error distribution given by the adjoint-based error estimator, h-or p-refinement is chosen based on the smoothness of the solution which can be quantified by properly-chosen smoothness indicators. Numerical results are shown for inviscid subsonic and transonic, and laminar viscous flow around the NACA0012 airfoil.
This work focuses on the extension of the recently introduced Spectral Difference Method to viscous flow. The spectral difference method is a conservative pseudo-spectral scheme based on a local collocation on unstructured elements. Recently results for scalar transport equations and the Euler equations have been presented. For the extension to viscous flow several techniques are investigated, such as a central discretization and a split upwind/downwind discretization, akin to the procedure used in the LDG method.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.