Implicit-explicit Godunov schemes for unsteady gas dynamics
Hybrid implicit-explicit schemes are developed for Eulerian hydrodynamics in one and two space dimensions. The hybridization is a continuous switch and operates on each characteristic field separately. The explicit scheme is a version of the second order Godunov scheme; the implicit method is only first order accurate in time but leads to second order accurate steady states. This methodology is developed for linear advection, nonlinear scalar problems, hyperbolic constant co-efficient systems, and for gas dynamics. Truncation error and stability analyses are done for the linear cases. This implicit-explicit strategy is intended for problems with spatially or temporally localized stiffness in wave speeds. By stiffness we mean that the high speed modes contain very little energy, yet they determine the explicit time step through the CFL condition. For hydrodynamics, the main examples are nearly incompressible flow, flows with embedded boundary layers, and magnetohydrodynamics; the latter two examples are not treated here. Several numerical results are presented to demonstrate this method. These include, stable numerical shocks at very high CFL numbers, one-dimensional flow in a duct, and low Mach number shear layers.
- Research Organization:
- Maryland Univ., College Park, MD (United States)
- OSTI ID:
- 121352
- Country of Publication:
- United States
- Language:
- English
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