M. J. Berger and A. Jameson. Automatic adaptive grid refinement for the euler equations. American Institute of Aeronautics and Astronautics, 23(4), 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....automatically determining where regions of grid refinement should be positioned. Adaptive mesh refinement (AMR) methods modeled after work by Berger [9] have been applied to systems of partial differential equations by Berger and Oliger [12] to the steady Euler equations by Berger and Jameson [11], and to the time dependent equations by Berger and Colella [10] Recent works have also included AMR in methods for the two and three dimensional incompressible fluid systems [1] 35] The goal of developing a fully automatic algorithm for AMR in incompressible flow simulations will likely ....

M. J. Berger and A. Jameson. Automatic adaptive grid refinement for the euler equations. AIAA J., 23:561--568, 1985.

....used for many grid problems have an accuracy of order h 2 . The accuracies are also proportional to the values of the derivatives of the variables. In regions of discontinuity, such as shock fronts, methods of order h are used. See Sod (1976) Lapidus (1967) Berger (1982) Berger (1984) Berger (1985),Berger (1987) and Press, Flannery, Teukosky, and Vetterling (1986) Stoer and Bulirsch (1984) With accuracy of order h 2 , the error in the numerical approximation is proportional to the dimensions of the cell to the second power. Thus, decreasing the size of a cell by 1 2 in a given direction ....

Berger, M. and Jameson, A. (1985) Automatic Adaptive Grid Refinement for the Euler Equations. American Institute of Aeronautics and Astronautics 23(4), p. 561.

....in some way use an estimate of the solution error. Then a threshold for refinement is set either by experience or by information obtained from the distribution of the error. Refinement of this type has been carried out on triangular tetrahedral grids [34, 43, 64] and quadrilateral hexahedral grids [7, 17, 36, 40, 59, 64] or a mixture of both [38, 47] This refinement is most often isotropic, but anisotropic (directional) refinement is also a viable option. 1, 14, 24, 55] 1.3 Cartesian Grid Methods An approach which is becoming more popular is the use of non body fitted unstructured grids, specifically ....

M. J. Berger and A. Jameson, "Automatic adaptive grid refinement for the Euler equations," AIAA Journal, vol. 23, 1985.

....face is to construct a triangular or quadrilateral mesh which respects a given riemannian metric map. Basically, two different approaches can be envisaged to address the adaptive triangular mesh generation problem of a given domain: ffl mesh optimization using refinement and derefinement tools [2, 18, 8] and ffl mesh reconstruction of the whole domain [4] For both cases, numerous algorithms have been proposed which appear to give satisfactory results, in particular when anisotropic specifications are required. There exists mainly two approaches (direct and indirect) concerning the generation of ....

M.J. Berger and A. Jameson, Automatic adaptive grid refinement for Euler equations, AIAA J. , vol 23, no 4, pp. 561--568, 1985.

.... the number of elements required to capture the behavior of the underlying physical phenomenon [16, 18, 19, 26] Basically, two different approaches can be envisaged to address the adaptive mesh generation problem of a given domain: ffl mesh optimization using refinement and derefinement tools [2, 21] and ffl mesh reconstruction of the whole domain [4] For both cases, numerous algorithms have been proposed which appear to give satisfactory results, in particular when anisotropic specifications are required. Two different approaches (direct and indirect) are used for the generation of ....

M.J. Berger and A. Jameson, Automatic adaptive grid refinement for Euler equations, AIAA J. , vol 23, no 4, pp. 561--568, 1985.

....of the computational domain rather than individual cells, again recursively applying this idea to allow increased resolution in some regions. This approach, illustrated in Fig. 6. 1, was pioneered by Berger and Oliger [27] and has been developed further by Berger and coworkers [19] 25] 28] [26]. Refinement on rectangular patches has the advantage that the data structures remain relatively simple, and consist of a nested set of grids. On each grid a standard finite volume method is used to sweep over the grid, though a certain amount of additional work must then be done at the interface ....

M. Berger and A. Jameson. Automatic adaptive grid refinement for the Euler equations. AIAA J., 23:561--568, 1985.

....high order non oscillatory schemes. In multi dimensional flow simulations, global reduction of the mesh interval can be prohibitively expensive, motivating the use of adaptive mesh refinement procedures which reduce the local mesh width h if there is an indication that the error is too large [25, 45, 117, 71, 155, 111, 147]. In such h refinement methods, simple error indicators such as local solution gradients may be used. Alternatively, the discretization error may be estimated by comparing quantities calculated with two mesh widths, say on the current mesh and a coarser mesh with double the mesh interval. ....

M. Berger and A. Jameson, Automatic adaptive grid refinement for the Euler equations, AIAA Journal, 23 (1985), pp. 561--568.

No context found.

M. Berger and A. Jameson, Automatic adaptive grid refinement for the Euler equations, AIAA J., 23 (1985), pp. 561--568.

No context found.

M. J. Berger and A. Jameson. Automatic adaptive grid refinement for the euler equations. American Institute of Aeronautics and Astronautics, 23(4), 1985.

No context found.

M.J. Berger and A. Jameson. Automatic adaptive grid refinement for the Euler equations. AIAA Journal, 23:561--568, 1985.

No context found.

Berger, M.J. and Jameson, A: "Automatic adaptive grid refinement for the Euler equations", AIAA Journal, 23(4):561--568, 1985.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC