  When solving compressible multi-material flow problems, an unresolved
challenge is the computation of advective fluxes across material interfaces
that separate drastically different thermodynamic states and relations. A
popular idea in this regard is to locally construct bimaterial Riemann
problems, and to apply their exact solutions in flux computation. For general
equations of state, however, finding the exact solution of a Riemann problem is
expensive as it requires nested loops. Multiplied by the large number of
Riemann problems constructed during a simulation, the computational cost often
becomes prohibitive. The work presented in this paper aims to accelerate the
solution of bimaterial Riemann problems without introducing approximations or
offline precomputation tasks. The basic idea is to exploit some special
properties of the Riemann problem equations, and to recycle previous solutions
as much as possible. Following this idea, four acceleration methods are
developed, including (1) a change of integration variable through rarefaction
fans, (2) storing and reusing integration trajectory data, (3) step size
adaptation, and (4) constructing an R-tree on the fly to generate initial
guesses. The performance of these acceleration methods are assessed using four
example problems in underwater explosion, laser-induced cavitation, and
hypervelocity impact. These problems exhibit strong shock waves, large
interface deformation, contact of multiple (>2) interfaces, and interaction
between gases and condensed matters. In these challenging cases, the solution
of bimaterial Riemann problems is accelerated by 37 to 87 times. As a result,
the total cost of advective flux computation, which includes the exact Riemann
problem solution at material interfaces and the numerical flux calculation over
the entire computational domain, is accelerated by 18 to 81 times.
