In this paper, we introduce a discontinuous Finite Element formulation on simplicial unstructured meshes for the study of free surface flows based on the fully nonlinear and weakly dispersive GreenNaghdi equations. Working with a new class of asymptotically equivalent equations, which have a simplified analytical structure, we consider a decoupling strategy: we approximate the solutions of the ...

A new modified Galerkin / Finite Element Method is proposed for the numerical solution of the fully nonlinear shallow water wave equations. The new numerical method allows the use of low-order Lagrange finite element spaces, despite the fact that the system contains third order spatial partial derivatives for the depth averaged velocity of the fluid. After studying the efficacy and the conserva...

A nonlinear extension of the Caginalp phase field system is considered that takes thermal memory into account. The resulting model, which a first-order approximation thermodynamically consistent system, inspired by theories developed Green and Naghdi. Two equations, from dynamics universal balance law for internal energy, are written in terms variable (representing non-conserved order parameter...

We propose a system of first-order balance laws that describe the propagation internal solitary waves in multilayer stratified shallow water with non-hydrostatic pressure upper and lower layers. The construction this model is based on use additional variables, which make it possible to approximate Green–Naghdi-type dispersive equations by system. In Boussinesq approximation, governing allow one...

We propose a new family of finite element methods for the Naghdi shell model, one method associated with each nonnegative integer k. The methods are based on a nonstandard mixed formulation, and the kth method employs triangular Lagrange finite elements of degree k+2 augmented by bubble functions of degree k+ 3 for both the displacement and rotation variables, and discontinuous piecewise polyno...

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...

Abstract In this investigation, a computational analysis is conducted to study magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium subjected periodic heat flow in the presence of continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, new generalized model has been investigated address considered problem. introduced can be form...