We study the relevance of various scalar equations, such as inviscid Burgers’, Korteweg-de Vries (KdV), extended KdV, and higher order equations (of Camassa-Holm type), as asymptotic models for the propagation of internal waves in a two-fluid system. These scalar evolution equations may be justified with two approaches. The first method consists in approximating the flow with two decoupled, cou...

The propagation of magneto-thermoelastic disturbances in an elastic half-space caused by the application of a thermal shock on the stress-free bounding surface in contact with vacuum is investigated. The theory of thermoelasticity III proposed by Green and Naghdi is used to study the interaction between elastic, thermal, and magnetic fields. Small-time approximations of solutions for displaceme...

The equations of motion of lossless compressible nonclassical fluids under the so-called Green–Naghdi theory are considered for two classes of barotropic fluids: (i) perfect gases and (ii) liquids obeying a quadratic equation of state. An exact reduction in terms of a scalar acoustic potential and the (scalar) thermal displacement is achieved. Properties and simplifications of these model nonli...

Abstract In this paper, we derive new shallow asymptotic models for the free boundary plasma-vacuum problem governed by magnetohydrodynamic equations which are vital when describing large-scale processes in flows of astrophysical plasma. More precisely, present magnetic analogue 2D Green–Naghdi water waves under a weak pressure assumption presence weakly sheared vorticity and currents. Our meth...

Extended shallow water wave equations are derived, using the method of asymptotic expansions, from Euler (or wave) equations. These extended models valid one order beyond usual weakly nonlinear, long approximation, incorporating all appropriate dispersive and nonlinear terms. Specifically, first we derive Korteweg–de Vries (KdV) equation, then proceed with Benjamin–Bona–Mahony Camassa–Holm in (...

In this paper, we present a fully discrete second-order finite-difference scheme with fast evaluation of the convolution involved in absorbing boundary conditions to solve one-dimensional linearized Green-Naghdi system. The Padé expansion square-root function complex plane is used implement convolution. By introducing constant damping parameter into governing equations, convergence analysis dev...

We consider the design of nite element methods for the Naghdi shell model in the case when the deformation is bending dominated. Two formulations based on stabilizing techniques are introduced and it is proved that they are stable, hence free from locking. The theoretical estimates are connrmed by numerical benchmark studies. M ethodes d' el ements nis stabilis ees pour les coques a exion domin...

Abstract Hydroelastic responses of floating elastic surfaces to incident nonlinear waves solitary and cnoidal type are studied. There N number the deformable surfaces, these represented by thin plates variable properties different sizes rigidity. The coupled motion fluid solved simultaneously within framework linear beam theory for structures Level I Green–Naghdi fluid. water surface elevation,...