A comparative study of the efficiency of jet schemes

We present two versions of third order accurate jet schemes, which achieve high order accuracy by tracking derivative information of the solution along characteristic curves. For a benchmark linear advection problem, the efficiency of jet schemes is compared with WENO and Discontinuous Galerkin methods of the same order. Moreover, the performance of various schemes in tracking solution contours is investigated. It is demonstrated that jet schemes possess the simplicity and speed of WENO schemes, while showing several of the advantages as well as the accuracy of DG methods.

[1]  Bernardo Cockburn.  An introduction to the Discontinuous Galerkin method for convection-dominated problems , 1998 .

[2]  Benjamin Seibold,et al.  Jet schemes for advection problems , 2011, 1101.5374.

[3]  Rune B. Lyngsø,et al.  Lecture Notes I , 2008 .

[4]  Chi-Wang Shu,et al.  Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems , 2001, J. Sci. Comput..

[5]  Chi-Wang Shu,et al.  The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems , 1998 .

[6]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[7]  Chi-Wang Shu,et al.  Strong Stability-Preserving High-Order Time Discretization Methods , 2001, SIAM Rev..

[8]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[9]  T. Taylor.  LOW REYNOLDS NUMBER FLOWS , 1968 .

[10]  J. Heller,et al.  An Unmixing Demonstration , 1960 .

[11]  Benjamin Seibold,et al.  A gradient-augmented level set method with an optimally local, coherent advection scheme , 2009, J. Comput. Phys..

[12]  S. Osher,et al.  Weighted essentially non-oscillatory schemes , 1994 .

[13]  R. LeVeque.  High-resolution conservative algorithms for advection in incompressible flow , 1996 .

[14]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[15]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[16]  W. H. Reed,et al.  Triangular mesh methods for the neutron transport equation , 1973 .

[17]  P. Colella,et al.  A second-order projection method for the incompressible navier-stokes equations , 1989 .

[18]  Chi-Wang Shu,et al.  Total variation diminishing Runge-Kutta schemes , 1998, Math. Comput..