Advection-reaction type partial differential equations model a wide variety of phenomena in several disciplines in physics, chemistry, environmental sciences, geometry, financial mathematics and many others. Generally, these non-linear inhomo-geneous equations must be solved in complicated multi-dimensional domains and thus analytical solutions are only available under very special circumstance...

This talk will come in four parts. First, I will introduce the Riemann hypothesis (RH) as it was first introduced, using the Riemann zeta function, and discuss briefly its connection to number theory and prime numbers. Second, I will make this connection explicit by discussion a famous problem equivalent to RH. Third, I will examine the generalised Riemann hypothesis (GRH) and, finally, will li...

We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics [6] for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary differential equation arising from the self-similarity condition along rarefaction waves, in a similar way as in purely normal flow. The dependence of the solution ...

Numerical results are presented for the shock-boundary layer interactions in a hypersonic flow over a sharp leading edge compression corner. In this study, a second- order Godunov type scheme based on solving a Generalized Riemann Problem (GRP) at each cell interface is used to solve thin shear layer approximation of laminar Navier-Stokes (N-S) equations. The calculated flow-field shows general...

This paper presents a numerical technique to approximate the Rayleigh–Stokes model for generalised Maxwell fluid formulated in Riemann–Liouville sense. The proposed method consists of two stages. First, time discretization problem is accomplished by using finite difference. Second, space obtained means predictor–corrector method. unconditional stability result and convergence analysis are analy...

Riemann-Problem and Level-Set Approaches for Homentropic Two-Fluid Flow Computations B. Koren,∗ M. R. Lewis,∗,1 E. H. van Brummelen,∗,2 and B. van Leer†,1 ∗CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands; and †University of Michigan, Department of Aerospace Engineering, Ann Arbor, Michigan 48109-2140 E-mail: [email protected], [email protected], [email protected], and br...

where t>0, o o < x < o o , U(t, x)=(u(t, x), v(t, x)), and the function F(U)= (f(u, v), g(u, v)) is smooth. GLIMM [2] has proved existence of a weak solution provided that the variation of the initial data Uo(x) is small. GLIMM & LAX [3] then improved this result by requiring that the oscillation of Uo(x) be small. SMOLLER [7] has proved the existence of a weak solution provided that Uo(x ) is ...