Total-Variation-Diminishing Implicit-Explicit Runge-Kutta Methods for the Simulation of Double-Diffusive Convection in Astrophysics
Jun, 2011
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Abstract: (arXiv)
We put forward the use of total-variation-diminishing implicit-explicit Runge-Kutta methods for the time integration of the equations of motion associated with the semiconvection problem in the simulation of stellar convection. The fully compressible Navier-Stokes equation augmented by continuity and total energy equations and an equation of state describing the relation between the thermodynamic quantities is semi-discretized in space by essentially non-oscillatory schemes and dissipative finite difference methods, and subsequently integrated in time by Runge-Kutta methods which are constructed such as to reduce the total variation in the spatial profile in the course of time integration under certain restrictions on the time step-size. We analyze the stability, accuracy and dissipativity of the time integrators and demonstrate that the most successful methods yield a substantial gain in computational efficiency as compared to classical explicit Runge-Kutta methods.Note:
- 37 pages, 15 figures, 12 tables, to be submitted to J. Comput. Phys
- 47.11.-j
- 97.10.Sj
- 02.70.-c
- Hydrodynamics
- Stellar convection and pulsation
- Double-diffusive convection
- Numerical methods
- Total-variation-diminishing
- Strong stability preserving
- TVD
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