In this paper, the numerical error of two widely used methods for remapping of discrete quantities from one computational mesh to another is investigated. We compare the intuitive, but resource intensive method utilizing intersections of computational cells with the faster and simpler swept-region-based method. Both algorithms are formally second order accurate, however, they are known to produce slightly different quantity profiles in practical applications. The second-order estimate of the error formula is constructed algebraically for both algorithms so that their local accuracy can be evaluated. This general estimate is then used to assess the dependence of the performance of both methods on parameters such as the second derivatives of the remapped distribution, mesh geometry or mesh movement. Due to the complexity of such analysis, it is performed on a set of simplified elementary mesh patterns such as cell corner expansion, rotation or shear. On selected numerical tests it is demonstrated that the swept-based method can distort a symmetric quantity distribution more substantially than the intersection-based approach when the computational mesh moves in an unsuitable direction.

This paper extends an algorithm of P1-conservative interpolation on triangular meshes to tetrahedral meshes and thus constructs an approach of solution reconstruction for three-dimensional problems. The conservation property is achieved by local mesh intersection and the mass of a tetrahedron of the current mesh is calculated by the integral on its intersection with the background mesh. For each current tetrahedron, the overlapped background tetrahedrons are detected efficiently. A mesh intersection algorithm is proposed to construct the intersection of a current tetrahedron with the overlapped background tetrahedron and mesh the intersection region by tetrahedrons. A localization algorithm is employed to search the host units in background mesh for each vertex of the current mesh. In order to enforce the maximum principle and avoid the loss of monotonicity, correction of nodal interpolated solution on tetrahedral meshes is given. The performance of the present solution reconstruction method is verified by numerical experiments on several analytic functions and the solution of the flow around a sphere.

A two-dimensional numerical scheme for the compressible Euler equations is presented and applied here to the simulation of exemplary compressible vortical flows. The proposed approach allows to perform computations on unstructured moving grids with adaptation, which is required to capture complex features of the flow-field. Grid adaptation is driven by suitable error indicators based on the Mach number and by element-quality constraints as well. At the new time level, the computational grid is obtained by a suitable combination of grid smoothing, edge-swapping, grid refinement and de-refinement. The grid modifications—including topology modification due to edge-swapping or the insertion/deletion of a new grid node—are interpreted at the flow solver level as continuous (in time) deformations of suitably-defined node-centered finite volumes. The solution over the new grid is obtained without explicitly resorting to interpolation techniques, since the definition of suitable interface velocities allows one to determine the new solution by simple integration of the Arbitrary Lagrangian-Eulerian formulation of the flow equations. Numerical simulations of the steady oblique-shock problem, of the steady transonic flow and of the start-up unsteady flow around the NACA 0012 airfoil are presented to assess the scheme capabilities to describe these flows accurately.

This paper extends the adaptive moving mesh method developed by Tang and Tang [36] to two-dimensional (2D) relativistic hydrodynamic (RHD) equations. The algorithm consists of two “independent” parts: the time evolution of the RHD equations and the (static) mesh iteration redistribution. In the first part, the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing equations. The second part is an iterative procedure. In each iteration, the mesh points are first redistributed, and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way. Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.