Numerical comparison of the method of transport to a standard scheme

In previous joint work with Zimmermann, we derived Fey's method of transport (MoT), a multidimensional flux vector splitting scheme, from gas kinetic theory via quadrature. Now we present a number of numerical tests in one and two space dimensions showing that similarly to many other flux vector splitting and kinetic schemes, the MoT is very dissipative. In order to quantify its numerical dissipation, we compare the second order MoT-ICE [J. Comput. Phys. 164(2) (2000) 283] to the classical, very simple, and at the same time very robust Harten-Lax-van Leer (HLL) scheme (also in a second order version), whose most significant drawback is its comparatively high dissipativity. Our numerical experiments indicate that the MoT-ICE is approximately as dissipative as the much cheaper HLL scheme. Recall that the HLL scheme does not suffer from any of the known multidimensional instabilities, which have been a prime motivation for the development of Riemann solver free schemes.