Space–Time Adaptive Solution of First Order PDES |
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Authors: | Lars Ferm Per Lötstedt |
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Affiliation: | (1) Department of Information Technology, Division of Scientific Computing, Uppsala University, SE-75105 Uppsala, Sweden |
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Abstract: | An explicit time-stepping method is developed for adaptive solution of time-dependent partial differential equations with
first order derivatives. The space is partitioned into blocks and the grid is refined and coarsened in these blocks. The equations
are integrated in time by a Runge–Kutta–Fehlberg (RKF) method. The local errors in space and time are estimated and the time
and space steps are determined by these estimates. The method is shown to be stable if one-sided space discretizations are
used. Examples such as the wave equation, Burgers’ equation, and the Euler equations in one space dimension with discontinuous
solutions illustrate the method. |
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Keywords: | Runge– Kutta– Fehlberg method shock problems space adaptation time adaptation |
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