|An Upwind Slope Limiter for PPM that Preserves Monotonicity in Magnetohydrodynamics
|444, 5th International Conference of Numerical Modeling of Space Plasma Flows (ASTRONUM 2010)
|We introduce a hybridized slope limiter for PPM that combines a new upwind
biased slope limiter with a conventional TVD slope limiter. We
demonstrate that this hybrid upwind limiter reduces spurious
numerical oscillations near discontinuities, and therefore can
compute sharp, monotonized profiles in compressible flows when using PPM, especially in
Magnetohydrodynamics (MHD) slowly moving shock regions.
Our proposed approach first detects a local, slowly moving shock, and considers
an upwind direction to compute a monotonicity-preserving slope limiter.
This new approach, in addition to improving the numerical solutions in
MHD to levels that reduce (or eliminate) such oscillatory behaviors,
while preserving sharp discontinuities in MHD, is also simple to
implement. The method described in this paper has been
verified against the results from other high-resolution
shock-capturing (HRSC) methods such as MUSCL and WENO schemes in