Finite element methods are used to solve a nonlinear system of partial diierential equations which models incompressible miscible displacement of one uid by another in porous media. From a backward nite diierence discretization we deene a sequentially implicit time-stepping algorithm which uncouples the system. The Galerkin method is employed to approximate the pressure, and improvement velocit...

A new meshless method for solving nonlinear boundary value problems, based on the local boundary integral equation (LBIE) method and the moving least squares approximation, is proposed in the present paper. The total formulation and a rate formulation are developed for the implementation of the present method. The present method does not need domain and boundary elements to deal with the volume...

Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions PDEs often do not satisfy requisite physical properties, such as positivity or monotonicity. Such invalid pose both modeling challenges, since the interpretation of simulation results is possible, computatio...

This work uses a higher-order discontinuous-Galerkin finite-element method to solve the compressible Navier-Stokes equations [1,2]. The unsteady Navier-Stokes equations are discretized using a non-linearly stable space-time entropyvariable formulation. The inviscid flux is computed using the approximate Riemann solver of Ismail and Roe [3]. The viscous fluxes are computed using an interior pena...

In the present study, nonlinear free vibration behavior of nanobeam subjected to magnetic field is investigated based on Eringen’s nonlocal elasticity and Euler–Bernoulli beam theory. The Hamilton’s principal is adopted to derive the governing equations together with Euler–Bernoulli beam theory and the von-Kármán’s nonlinear strain–displacement relationships. An approximate analytical solution ...