In this research, we studied numerically nonlinear evolutions of the Kelvin-Helmholtz instability (KHI) with and without thermal conduction, aka, the ablative KHI (AKHI) and the classical KHI (CKHI). The second order thermal conduction term with a variable thermal conductivity coefficient is added to the energy equation in the Euler equations in the AKHI to investigate the effect of thermal conduction on the evolution of large and small scale structures within the shear layer which separate the fluids with different velocities. The inviscid hyperbolic flux of Euler equation is computed via the classical fifth order weighted essentially nonoscillatory finite difference scheme and the temperature is solved by an implicit fourth order finite difference scheme with variable coefficients in the second order parabolic term to avoid severe time step restriction imposed by the stability of the numerical scheme. As opposed to the CKHI, fine scale structures such as the vortical structures are suppressed from forming in the AKHI due to the dissipative nature of the second order thermal conduction term. With a single-mode sinusoidal interface perturbation, the results of simulations show that the growth of higher harmonics is effectively suppressed and the flow is stabilized by the thermal conduction. With a two-mode sinusoidal interface perturbation, the vortex pairing is strengthened by the thermal conduction which would allow the formation of large-scale structures and enhance the mixing of materials. In summary, our numerical studies show that thermal conduction can have strong influence on the nonlinear evolutions of the KHI. Thus, it should be included in applications where thermal conduction plays an important role, such as the formation of large-scale structures in the high energy density physics and astrophysics.
Scopus Subject Areas
- Condensed Matter Physics