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Paper: An Upwind Slope Limiter for PPM that Preserves Monotonicity in Magnetohydrodynamics
Volume: 444, 5th International Conference of Numerical Modeling of Space Plasma Flows (ASTRONUM 2010)
Page: 236
Authors: Lee, D.
Abstract: 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 FLASH.
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