The stability and accuracy of EPIC algorithms. (English) Zbl 0667.76156
In the absence of particle discretisation effects (quadrature errors) EPIC algorithms give accurate and unconditionally stable schemes for integrating kinematic fluid and MHD equations. If particle discretisation is introduced as a consistently applied trapezium rule quadrature, the unconditional stability is retained. However, it is shown that not all quadratures lead to stable schemes. General results on linear stability are given. An analysis of dispersive and dissipative effects of finite particle number is presented, and the efficacy of the algorithm is illustrated by kinematics and dynamic test problems. The kinematic test with discrete particles showed unexpected stability and accuracy for large Courant numbers.
MSC:
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
References:
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