Abstract: One of the hard nuts to crack in computational fluid dynamics is how to simultaneously
resolve both smooth (vortex, acoustic wave) and discontinuous (shock, contact jump, material
interface) flow structures with high fidelity. The currently available high-resolution schemes
are devised under the mainstream Godunov finite volume framework which combines
polynomial-based reconstruction and nonlinear limiting projection so as to compromise between
spurious oscillation and numerical dissipation. In spite of great success in many applications, it is
found that the existing methods of this sort can hardly provide adequate solution quality for either
smooth or non-smooth solution due to excessive numerical dissipation.
In this talk, we present a novel paradigm, so-called Boundary Variation Diminishing (BVD) principle,
to design high-fidelity finite volume schemes to capture both smooth and non-smooth flow structures
with superior solution quality. The BVD principle minimizes the jumps of the reconstructed physical
variables at cell boundaries, and thus effectively reduces the dissipation errors. More profoundly,
the BVD principle provides a completely new alternative to the conventional limiting-projection
approach to eliminate numerical oscillation. With proper BVD-admissible functions and BVD algorithms,
we have developed a new class of numerical schemes of great practical significance for compressible
and interfacial multiphase flows. The numerical schemes have been extensively verified with various
benchmark tests of single and multiphase compressible flows involving strong discontinuities and
complex flow structure of broad-band scales.
Biographical sketch of Prof. Feng Xiao: Prof. Xiao got his doctoral degree in science from Tokyo
Institute of Technology (Tokyo Tech) in 1996. After three years in RIKEN as a special post-doctoral
researcher, he joined Tokyo Tech in 1999, and now is a full professor in the department of mechanical
Prof. Xiao has been recently engaged in researches in computational fluid dynamics (CFD), geophysical
fluid dynamic modeling, computational physics, as well as CFD applications in engineering, he has authored
or co-authored over 100 papers in academic journals and over 200 presentations in conferences and symposia.
He is a fellow of Japan Society of Mechanical Engineers (JSME), and a recipient of the JSME Computational
Mechanics Achievement Award, JACM Computational Mechanics Award, JACM Fellow Award, among others.
He was honored as a visiting fellow of Isaac Newton Institute for Mathematical Sciences (Cambridge) in 2012.
Prof. Xiao is currently serving the executive editor of Journal of Computational Physics (JCP).