Central Schemes on Overlapping Cells
Nessyahu and Tadmor's central scheme (J. Comput. Phys, 87(1990)) has the benefi t of not using Riemann solvers or characteristic decomposition for solving hyperbolic conservation laws and related convection diffusion equations. But the staggered averaging causes large dissipation when the time step size is small comparing to the mesh size. The recent work of Kurganov and Tadmor (J. Comput. Phys, 160(2000)) overcomes the problem by use of a variable control volume and obtains a semi-discrete non-staggered central scheme. Motivated by this work, we introduce overlapping cell averages of the solution at the same discrete time level, and develop a simple alternative technique to control the O(1/∆t) dependence of the dissipation. Semi-discrete form of the central scheme can also be obtained to which the TVD Runge-Kutta time discretization of Shu and Osher (J. Comput. Phys, 77(1988)) can be applied. This technique is essentially independent of the reconstruction and the shape of the mesh, thus could also be useful for unstructured mesh. The overlapping cell representation of the solution also opens new possibilities for reconstructions. Generally more compact reconstruction can be achieved. We demonstrate through numerical examples that combining two classes of the overlapping cells in the reconstruction can achieve higher resolution.
Showing items related by title, author, creator and subject.
Flowers, Mallory Elise (Georgia Institute of Technology, 2017-08-02)This dissertation examines evidence on the effectiveness of voluntary certification programs in the built environment. Drawing on unique data from buildings certified under the Leadership in Energy and Environmental Design ...
Evaluation of targeting schemes for complement-modulating, strain-selective antimicrobial microparticles Bellavia, Michael (Georgia Institute of Technology, 2018-04-30)Here we present bifunctional microparticles that bind Escherichia coli (E. coli) bacteria via a cell membrane constituent while also activating the classical complement pathway. Carboxylated polystyrene microparticles 1 ...
Studies in the mass 160 decay chain. gamma-ray and conversion electron spectroscopy for the 160lu-160yb, 160yb-160tm, 160tm-160er decay schemes. Brown, Nathaniel J. (Georgia Institute of Technology, 2008-12-16)Excited states in the transitional nucleus 160Yb have been studied using gamma-ray and conversion electron spectroscopy following the beta+/EC decay of 160Lu. Excited states in the nuclei 160Tm and 160Er have been studied ...