A new piecewise cubic method (PCM) for compressible fluid dynamics

Research Group: H. Faller (ENS, France & UCSC), Youngjun Lee, Adam Reyes, D. Lee (UCSC)

We develop a new fourth-order shock capturing algorithm suitable for both finite difference and finite volume methods. The idea is to improve the 3rd-order piecewise parabolic method (PPM) algorithm to a 4th-order scheme using a monotone conserving cubic polynomial.