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Accurate two and three dimensional interpolation for particle mesh calculations
Jet schemes for advection problems
1. | Temple University, Department of Mathematics, 1805 North Broad Street Philadelphia, PA 19122 |
2. | Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, United States |
3. | Department of Mathematics and Statistics, McGill University, 805 Sherbrooke W., Montreal, QC, H3A 2K6, Canada |
References:
[1] |
D. Adalsteinsson and J. A. Sethian, The fast construction of extension velocities in level set methods, J. Comput. Phys., 148 (1999), 2-22.
doi: 10.1006/jcph.1998.6090. |
[2] |
A. V. Arutyunov, "Optimality Conditions: Abnormal and Degenerate Problems," Mathematics and its Applications, 526, Kluwer Academic Publishers, Dordrecht, 2000. |
[3] |
J. B. Bell, P. Colella and H. Glaz, A second-order projection method for the incompressible Navier-Stokes equations, J. Comput. Phys., 85 (1989), 257-283.
doi: 10.1016/0021-9991(89)90151-4. |
[4] |
M. J. Berger and J. Oliger, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys., 53 (1984), 484-512.
doi: 10.1016/0021-9991(84)90073-1. |
[5] |
J. R. Cash and A. H. Karp, A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides, ACM Trans. Math. Software, 16 (1990), 201-222.
doi: 10.1145/79505.79507. |
[6] |
P. Chidyagwai, J.-C. Nave, R. R. Rosales and B. Seibold, A comparative study of the efficiency of jet schemes, Int. J. Numer. Anal. Model.-B, under review, 2011, arXiv:1104.0542. |
[7] |
B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems, SIAM J. Numer. Anal., 35 (1998), 2440-2463.
doi: 10.1137/S0036142997316712. |
[8] |
R. Courant, E. Isaacson and M. Rees, On the solution of nonlinear hyperbolic differential equations by finite differences, Comm. Pure Appl. Math., 5 (1952), 243-255.
doi: 10.1002/cpa.3160050303. |
[9] |
S. Gottlieb, On high order strong stability preserving Runge-Kutta and multi step time discretizations, J. Sci. Comput., 25 (2005), 105-128. |
[10] |
S. Gottlieb, D. I. Ketcheson and C.-W. Shu, High order strong stability preserving time discretizations, Journ. Sci. Computing, 38 (2009), 251-289.
doi: 10.1007/s10915-008-9239-z. |
[11] |
S. Gottlieb and C.-W. Shu, Total variation diminishing Runge-Kutta schemes, Math. Comp., 67 (1998), 73-85.
doi: 10.1090/S0025-5718-98-00913-2. |
[12] |
S. Gottlieb, C.-W. Shu and E. Tadmor, Strong stability-preserving high-order time discretization methods, SIAM Rev., 43 (2001), 89-112.
doi: 10.1137/S003614450036757X. |
[13] |
J. P. Heller, An unmixing demonstration, Am. J. Phys., 28 (1960), 348-353.
doi: 10.1119/1.1935802. |
[14] |
W. Hesthaven and T. Warburton, "Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applicationss," Texts in Applied Mathematics, 54, Springer, New York, 2008. |
[15] |
G.-S. Jiang and C.-W. Shu, Efficient implementation of weighted ENO schemes,, J. Comput. Phys., 126 (): 202.
|
[16] | |
[17] |
R. LeVeque, High-resolution conservative algorithms for advection in incompressible flow, SIAM J. Numer. Anal., 33 (1996), 627-665.
doi: 10.1137/0733033. |
[18] |
X.-D. Liu, S. Osher and T. Chan, Weighted essentially non-oscillatory schemes, J. Comput. Phys., 115 (1994), 200-212.
doi: 10.1006/jcph.1994.1187. |
[19] |
C.-H. Min and F. Gibou, A second order accurate level set method on non-graded adaptive cartesian grids, J. Comput. Phys., 225 (2007), 300-321.
doi: 10.1016/j.jcp.2006.11.034. |
[20] |
J. F. Nash, Jr., Arc structure of singularities, Duke Math. J., 81 (1995), 31-38.
doi: 10.1215/S0012-7094-95-08103-4. |
[21] |
J.-C. Nave, R. R. Rosales and B. Seibold, A gradient-augmented level set method with an optimally local, coherent advection scheme, J. Comput. Phys., 229 (2010), 3802-3827.
doi: 10.1016/j.jcp.2010.01.029. |
[22] |
S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), 12-49.
doi: 10.1016/0021-9991(88)90002-2. |
[23] |
W. H. Reed and T. R. Hill, Triangular mesh methods for the neutron transport equation, Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory, 1973. |
[24] |
C.-W. Shu, Total-variation-diminishing time discretizations, SIAM J. Sci. Statist. Comput., 9 (1988), 1073-1084.
doi: 10.1137/0909073. |
[25] |
C.-W. Shu and S. Osher, Efficient implementation of essentially nonoscillatory shock-capturing schemes, J. Comput. Phys., 77 (1988), 439-471.
doi: 10.1016/0021-9991(88)90177-5. |
[26] |
M. Sussman, P. Smereka and S. Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys., 114 (1994), 146-159.
doi: 10.1006/jcph.1994.1155. |
[27] |
G. I. Taylor, "Low Reynolds Number Flow," Movie, U.S. National Committee for Fluid Mechanics Films (NCFMF), 1961. |
[28] |
B. van Leer, Towards the ultimate conservative difference scheme I. The quest of monoticity, Springer Lecture Notes in Physics, 18 (1973), 163-168.
doi: 10.1007/BFb0118673. |
[29] |
B. van Leer, Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method, J. Comput. Phys., 32 (1979), 101-136.
doi: 10.1016/0021-9991(79)90145-1. |
show all references
References:
[1] |
D. Adalsteinsson and J. A. Sethian, The fast construction of extension velocities in level set methods, J. Comput. Phys., 148 (1999), 2-22.
doi: 10.1006/jcph.1998.6090. |
[2] |
A. V. Arutyunov, "Optimality Conditions: Abnormal and Degenerate Problems," Mathematics and its Applications, 526, Kluwer Academic Publishers, Dordrecht, 2000. |
[3] |
J. B. Bell, P. Colella and H. Glaz, A second-order projection method for the incompressible Navier-Stokes equations, J. Comput. Phys., 85 (1989), 257-283.
doi: 10.1016/0021-9991(89)90151-4. |
[4] |
M. J. Berger and J. Oliger, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys., 53 (1984), 484-512.
doi: 10.1016/0021-9991(84)90073-1. |
[5] |
J. R. Cash and A. H. Karp, A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides, ACM Trans. Math. Software, 16 (1990), 201-222.
doi: 10.1145/79505.79507. |
[6] |
P. Chidyagwai, J.-C. Nave, R. R. Rosales and B. Seibold, A comparative study of the efficiency of jet schemes, Int. J. Numer. Anal. Model.-B, under review, 2011, arXiv:1104.0542. |
[7] |
B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems, SIAM J. Numer. Anal., 35 (1998), 2440-2463.
doi: 10.1137/S0036142997316712. |
[8] |
R. Courant, E. Isaacson and M. Rees, On the solution of nonlinear hyperbolic differential equations by finite differences, Comm. Pure Appl. Math., 5 (1952), 243-255.
doi: 10.1002/cpa.3160050303. |
[9] |
S. Gottlieb, On high order strong stability preserving Runge-Kutta and multi step time discretizations, J. Sci. Comput., 25 (2005), 105-128. |
[10] |
S. Gottlieb, D. I. Ketcheson and C.-W. Shu, High order strong stability preserving time discretizations, Journ. Sci. Computing, 38 (2009), 251-289.
doi: 10.1007/s10915-008-9239-z. |
[11] |
S. Gottlieb and C.-W. Shu, Total variation diminishing Runge-Kutta schemes, Math. Comp., 67 (1998), 73-85.
doi: 10.1090/S0025-5718-98-00913-2. |
[12] |
S. Gottlieb, C.-W. Shu and E. Tadmor, Strong stability-preserving high-order time discretization methods, SIAM Rev., 43 (2001), 89-112.
doi: 10.1137/S003614450036757X. |
[13] |
J. P. Heller, An unmixing demonstration, Am. J. Phys., 28 (1960), 348-353.
doi: 10.1119/1.1935802. |
[14] |
W. Hesthaven and T. Warburton, "Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applicationss," Texts in Applied Mathematics, 54, Springer, New York, 2008. |
[15] |
G.-S. Jiang and C.-W. Shu, Efficient implementation of weighted ENO schemes,, J. Comput. Phys., 126 (): 202.
|
[16] | |
[17] |
R. LeVeque, High-resolution conservative algorithms for advection in incompressible flow, SIAM J. Numer. Anal., 33 (1996), 627-665.
doi: 10.1137/0733033. |
[18] |
X.-D. Liu, S. Osher and T. Chan, Weighted essentially non-oscillatory schemes, J. Comput. Phys., 115 (1994), 200-212.
doi: 10.1006/jcph.1994.1187. |
[19] |
C.-H. Min and F. Gibou, A second order accurate level set method on non-graded adaptive cartesian grids, J. Comput. Phys., 225 (2007), 300-321.
doi: 10.1016/j.jcp.2006.11.034. |
[20] |
J. F. Nash, Jr., Arc structure of singularities, Duke Math. J., 81 (1995), 31-38.
doi: 10.1215/S0012-7094-95-08103-4. |
[21] |
J.-C. Nave, R. R. Rosales and B. Seibold, A gradient-augmented level set method with an optimally local, coherent advection scheme, J. Comput. Phys., 229 (2010), 3802-3827.
doi: 10.1016/j.jcp.2010.01.029. |
[22] |
S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), 12-49.
doi: 10.1016/0021-9991(88)90002-2. |
[23] |
W. H. Reed and T. R. Hill, Triangular mesh methods for the neutron transport equation, Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory, 1973. |
[24] |
C.-W. Shu, Total-variation-diminishing time discretizations, SIAM J. Sci. Statist. Comput., 9 (1988), 1073-1084.
doi: 10.1137/0909073. |
[25] |
C.-W. Shu and S. Osher, Efficient implementation of essentially nonoscillatory shock-capturing schemes, J. Comput. Phys., 77 (1988), 439-471.
doi: 10.1016/0021-9991(88)90177-5. |
[26] |
M. Sussman, P. Smereka and S. Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys., 114 (1994), 146-159.
doi: 10.1006/jcph.1994.1155. |
[27] |
G. I. Taylor, "Low Reynolds Number Flow," Movie, U.S. National Committee for Fluid Mechanics Films (NCFMF), 1961. |
[28] |
B. van Leer, Towards the ultimate conservative difference scheme I. The quest of monoticity, Springer Lecture Notes in Physics, 18 (1973), 163-168.
doi: 10.1007/BFb0118673. |
[29] |
B. van Leer, Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method, J. Comput. Phys., 32 (1979), 101-136.
doi: 10.1016/0021-9991(79)90145-1. |
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