Quantifying Advantages of a Moving Mesh in Nuclear Hydrodynamics

Many astrophysical explosions, such as type Ia supernovae, classical novae, and X-ray bursts, are dominated by thermonuclear runaway. To model these processes accurately, one must evolve nuclear reactions concurrently with hydrodynamics. We present an application of the moving mesh technique to this field of computation with the aim of explicitly testing the advantages of the method against the fixed mesh case. By way of traditional Strang splitting, our work couples a 13 isotope nuclear reaction network to a 1D moving mesh, Cartesian geometry hydrodynamics code. We explore three reacting problems: an acoustic pulse, a burning shock, and an advecting deflagration. Additionally using the shock jump conditions, we semi-analytically solve the burning shock problem under the assumption of quick, complete burning with the hope of establishing a useful and easy to set-up test problem. Strong moving mesh advantages are found in advecting, deflagrating flame fronts, where the technique dramatically reduces numerical diffusion that would otherwise lead to very fast artificial deflagration.