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Abstract. The conservative front-tracking method developed in
[15, 16], with the 5th-order WENO scheme developed in [11] as
the underlying scheme, uses 1D hyperbolic onservation laws to describe the
motion of the interface and discretizes them by the Lax-Wendroff (LxW)
scheme in some way. In this paper, we use this method to simulate a single-mode
Richtmyer-Meshkov instability (RMI). The purpose is to test the ability of
this front-tracking method to simulate the RMI, especially its advantages
over capturing schemes. On a coarse grid the simulation gives a much better
result than the capturing simulation. The interface with roll-ups is well
resolved, the discontinuity in density is sharply represented without
width, and the smooth solution on the two sides of the interface is well
computed. This is because the method includes no numerical dissipation
across the tracked interface, and the numerical dispersion of the LxW
scheme for tracking the interface serves as a numerical surface tension,
which regularizes the interface in the simulation. However, in the
simulation on a finer grid, though the main structure of the interface is
well resolved, the discontinuity in density is sharply represented and the
smooth solution on the two sides of the interface is well computed, the
roll-ups of the interface develop complex, maybe incorrect, structures,
which finally terminates the simulation at an intermediate time. The reason
is that the LxW scheme for tracking the interface is not yet good enough
for regularizing the interface. In our future development of the method the
LxW scheme will be replaced with better schemes, such as the TVD schemes
that include numerical dissipation.
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