Abstract: The paper discusses the subinterval-based numerical
method for fractional derivative computations. It is now referred
to by its acronym – SubIval. The basis of the method is briefly
recalled. The ability of the method to be applied in time stepping
solvers is discussed. The possibility of implementing a time step size
adaptive solver is also mentioned. The solver is tested on a transient
circuit example. In order to display the accuracy of the solver –
the results have been compared with those obtained by means of a
semi-analytical method called gcdAlpha. The time step size adaptive
solver applying SubIval has been proven to be very accurate as
the results are very close to the referential solution. The solver is
currently able to solve FDE (fractional differential equations) with
various derivative orders for each equation and any type of source
time functions.
Abstract: The performance of high-resolution schemes is investigated for unsteady, inviscid and compressible multiphase flows. An Eulerian diffuse interface approach has been chosen for the simulation of multicomponent flow problems. The reduced fiveequation and seven equation models are used with HLL and HLLC approximation. The authors demonstrated the advantages and disadvantages of both seven equations and five equations models studying their performance with HLL and HLLC algorithms on simple test case. The seven equation model is based on two pressure, two velocity concept of Baer–Nunziato [10], while five equation model is based on the mixture velocity and pressure. The numerical evaluations of two variants of Riemann solvers have been conducted for the classical one-dimensional air-water shock tube and compared with analytical solution for error analysis.