The objective of this paper is to propose a hyperbolic relaxation technique for the dispersive Serre-Green-Naghdi equations (also known as fully non-linear Boussinesq equations) with full topography effects introduced in Green, A.E. and Naghdi, P.M. (J. Fluid Mech., 78, 237-246, 1976) Seabra-Santos el al Mec.h, 176, 117-134, 1997). This done by revisiting similar Guermond Comput. Phys., 399, 10...

Abstract We discuss models for flow in a class of generalized Navier–Stokes equations. The work concentrates on producing thermal convection, analysing these detail, and deriving critical Rayleigh wave numbers the onset convective fluid motion. In addition to linear instability theory we present careful analysis fully nonlinear stability theory. theories analysed all possess bi-Laplacian term n...

In the present work, a modified model of heat conduction including higher order of time derivative is derived by extending Green and Naghdi theory without energy dissipation. We introduce two phase lag times to include the thermal displacement gradient and the heat flux in the heat conduction and depict microscopic responses more precisely. The constructed model is applied to s...