We present some variants of Burgers-type equations for incompressible and isothermal planar flow of viscous non-Newtonian fluids based on the Cross, the Carreau and the power-law rheology models, and on a symmetry assumption on the flow. We numerically solve the associated traveling wave equations by using industrial data and in order to validate the models we prove existence and uniqueness of ...

In this paper, two-dimensional and axisymmetric, time dependent transonic and supersonic flows over a projectile overtaking a moving shock wave are considered. The flow is simulated numerically by solving full time averaged Navier-Stokes equations. The equations are linearized by Newton approach. The roe’s flux splitting method, second order central difference scheme for the diffusion terms, an...

A theoretical analysis of radial wave thermoacoustic engines in cylindrical resonators is developed. Impedance and pressure translation equations are presented for open sections of the resonator and for heat exchangers. Coupled first-order differential equations are given for pressure and impedance in the temperature gradient supporting engine section ~stack!. These quantities are used to calcu...

In this paper the propagation of harmonic plane waves in a homogeneous anisotropic magneto-piezothermoelastic diffusive body with fractional order derivative is studied. The governing equations for a homogeneous transversely isotropic body in the context of the theory of thermoelasticity with diffusion given by Sherief et al. [1] are considered as a special case. It is found that three types of...

We present fast, spatially dispersionless and unconditionally stable high-order solvers for Partial Differential Equations (PDEs) with variable coefficients in general smooth domains. Our solvers, which are based on (i) A certain “Fourier continuation” (FC) method for the resolution of the Gibbs phenomenon, together with (ii) A new, preconditioned, FC-based solver for two-point boundary value p...

Abstract. Under appropriate assumptions the energy of wave equations with damping and variable coefficients c(x)utt − div(b(x)∇u) + a(x)ut = h(x, t) has been shown to decay. Determining the decay rate for the higher order energies of the kth order spatial and time derivatives has been an open problem with the exception of some sparse results obtained for k = 1, 2. We establish the sharp gain in...