As underwater disturbances (natural or artificial) occur in the ocean, moving seawater crossing geomagnetic fields will produce weak circular currents. These currents can induce measurable magnetic fields, which might be useful for monitoring ocean internal waves using aeromagnetic survey. In this research, a spectral-element method (SEM) based on Gauss–Lobatto–Legendre (GLL) polynomials is pre...

This paper presents a Gauss Legendre quadrature method for numerical integration over the standard triangular surface: {(x, y) | 0 , 1, 1} x y x y ≤ ≤ + ≤ in the Cartesian two-dimensional (x, y) space. Mathematical transformation from (x, y) space to (ξ, η) space map the standard triangle in (x, y) space to a standard 2-square in (ξ, η) space: {(ξ, η)|–1 ≤ ξ, η ≤ 1}. This overcomes the difficul...

In this paper, we discuss the numerical solution of space fractional diffusion equations. The method of solution is based on using Chebyshev polynomials and finite difference with Gauss-Lobatto points. The validity and reliability of this scheme is tested by its application in various space fractional diffusion equations. The obtained results reveal that the proposed method is more accurate and...

We describe a new spectral multidomain method for the solution of the compressible Navier-Stokes equations. Within each subdomain, the method collocates the solution unknowns and the gradients at the nodes of the Gauss-Chebyshev quadrature. The total fluxes are evaluated at the nodes of the Gauss-Lobatto quadrature. Both conforming and non-conforming subdomain grids are allowed. Two examples ar...

Abstract. We consider a general class of systems of overdetermined differential-algebraic equations (ODAEs). We are particularly interested in extending the application of the symplectic Gauss methods to Hamiltonian and Lagrangian systems with holonomic constraints. For the numerical approximation to the solution to these ODAEs, we present specialized partitioned additive Runge– Kutta (SPARK) m...

and Applied Analysis 3 nonlinear term is treated with the Chebyshev collocation method. The time discretization is a classical Crank-Nicholson-leap-frog scheme. Yuan and Wu 43 extended the Legendre dual-Petrov-Galerkin method proposed by Shen 44 , further developed by Yuan et al. 45 to general fifth-order KdV-type equations with various nonlinear terms. The main aim of this paper is to propose ...

A novel numerical framework is discussed to simulate the time evolution of non-inertial particle size distributions (or number density functions) in flames. The generic form population balance equation considered featuring nucleation, surface growth/loss and agglomeration/coagulation. This first recast a that prone minimize spurious errors simulation collision integrals. Formally, this achieved...

The Meshless Local Petrov Galerkin (MLPG) method is used to solve the non-steady two dimensional Navier-Stokes equations. Transient laminar flow field calculations have been carried out in domains wherein certain surfaces have: (i) a sliding motion, (ii) a harmonic motion, (iii) an undulatory movement, and (iv) a contraction-expansion movement. The weak form of the governing equations has been ...