Solusi Persamaan Burgers Inviscid dengan Metode Pemisahan Variabel

Penelitian ini mengkaji tentang solusi persamaan Burgers Inviscid dengan metode pemisahan variabel. Tujuan dari penelitian ini adalah untuk mengetahui penyederhanaan sistem persamaan Navier-Stokes menjadi persamaan Burgers Inviscid, menemukan solusi persamaan Burgers Inviscid dengan metode pemisahan variabel, dan melakukan simulasi solusi persamaan dengan menggunakan software Maple18. Persamaan Burgers muncul sebagai penyederhanaan model yang rumit dari sistem persamaan Navier-Stokes. Persamaan Burgers adalah persamaan diferensial parsial hukum konservasi dan merupakan masalah hiperbolik, yaitu representasi nonlinier paling sederhana dari persamaan Navier-Stokes. Metode pemisahan variabel merupakan salah satu metode klasik yang efektif digunakan dalam menyelesaikan persamaan diferensial parsial dengan mengasumsikan untuk mendapatkan komponen x dan t. Kemudian akan dilakukan subtitusi pada persamaan diferensial, sehingga dengan cara ini akan didapatkan solusi persamaan diferensial parsial.Kata Kunci: Persamaan Burgers Inviscid, metode pemisahan variabel, persamaan Navier-StokesThis study examines the solution of Burgers Inviscid equation with variable separation method. The purpose of this study was to find out the simplification of the Navier-Stokes equation system into the Burgers Inviscid equation, find a solution to the Burgers Inviscid equation with the variable separation method, and simulate equation solutions using Maple18 software. The Burgers equation emerged as a complicated simplification of the Navier-Stokes equation system. The Burgers equation is a partial differential equation of conservation law and is a hyperbolic problem, i.e. the simplest nonlinear representation of the Navier-Stokes equation. The variable separation method is one of the classic methods that is effectively used in solving partial differential equations assuming to obtain the x and t components. Then there will be substitutions to differential equations, so that in this way there will be a partial differential equation solution.Keywords: Burgers Inviscid Equation, variable separation method, Navier-Stokes equations.

An Analytical Solution for the Interaction of Waves with Arrays of Circular Cylinders

This paper presents an analytical method to investigate the multiple scattering problem within arrays of vertical bottom-mounted circular cylinders subjected to linear incident waves. Based on the Laplace equation and boundary conditions on the seabed and surface, a formulation of a two-dimensional multiple scattering problem is first obtained by using the variable separation method. Furthermore, the analytical solution of the wave forces on multiple circular cylinders is derived, which consists of the incident wave force due to the linear incident wave and the scattered wave forces considering multiple scattering waves. The presented analytical solution is validated by comparing its results with a numerical method, and the result shows that the analytical solution is in good agreement with the numerical one. Finally, the multiple scattering analysis is conducted on arrays of cylinders with different incident wave numbers, distances between cylinders, and quantities.

Prediction of Frequency Response Function for Cylindrical Thin-Walled Workpiece with Fixture Support Constraints

Auxiliary fixtures are widely used to enhance the rigidity of cylindrical thin-walled workpieces (CTWWs) in the machining process. Nevertheless, the accurate and efficient prediction of frequency response function (FRF) for the workpiece-fixture system remains challenging due to the complicated contact constraints between workpiece and fixture. This paper proposes an analytical solution for the comprehensive FRF analysis of the CTWW-fixture system. Firstly, based on the vector mechanics, the mode shape functions of the workpiece are presented using the classical theory of thin shell. The variable separation method is utilized to deal with the inter-mode coupling of the workpiece. Secondly, the motion equation of the CTWW with fixture constraints is established using analytical mechanics from the viewpoint of energy balance. Finally, the FRFs of the CTWW-fixture system are derived by means of modal superposition. Experimental modal tests verify that the predicted FRFs are in good agreement with the measured curves.

General features of the linear crystalline morphology of accretion disks

In this paper, we analyze the so-called Master Equation of the linear backreaction of a plasma disk in the central object magnetic field, when small scale ripples are considered. This study allows to single out two relevant physical properties of the linear disk backreaction: (i) the appearance of a vertical growth of the magnetic flux perturbations; (ii) the emergence of sequence of magnetic field O-points, crucial for the triggering of local plasma instabilities. We first analyze a general Fourier approach to the solution of the addressed linear partial differential problem. This technique allows to show how the vertical gradient of the backreaction is, in general, inverted with respect to the background one. Instead, the fundamental harmonic solution constitutes a specific exception for which the background and the perturbed profiles are both decaying. Then, we study the linear partial differential system from the point of view of a general variable separation method. The obtained profile describes the crystalline behavior of the disk. Using a simple rescaling, the governing equation is reduced to the second-order differential Whittaker equation. The zeros of the radial magnetic field are found by using the solution written in terms Kummer functions. The possible implications of the obtained morphology of the disk magnetic profile are then discussed in view of the jet formation. GraphicAbstract

The application bispherical coordinate in Schrödinger equation for Mobius square plus modified Yukawa potential using Nikiforov Uvarov Functional Analysis (NUFA) method

<p class="Abstract">The application bispherical coordinates in Schrödinger equation for the Mobius square plus modified Yukawa potential have been obtained. The Schrödinger equation in bispherical coordinates for the separable Mobius square plus modified Yukawa potential consisting of the radial part and the angular part for the Mobius square plus modified Yukawa potential is solved using the variable separation method to reduce it to the radial part and angular part Schrödinger equation. The aim of this study was to solve the Schrödinger's equation of radial in bispherical coordinates for the Mobius square plus modified Yukawa potential using the Nikiforov Uvarov Functional Analysis (NUFA) method. Nikiforov Uvarov Functional Analysis (NUFA) method used to obtained energy spectrum equation and wave function for the Mobius square plus modified Yukawa potential. The result of energy spectrum equation for Mobius square plus modified Yukawa potential can be shown in Equation (50). The result of un-normalized wave function equation for Mobius square plus modified Yukawa potential can be shown in Table 1.</p>

A Method to Solve the Heat Transfer Problem in a Circular Duct With an Internal Longitudinal Fin

The heat transfer problem in a circular duct with an internal longitudinal fin is investigated under constant wall temperature. Different fin heights are considered. The problem is solved in two stages. In the first stage, the distribution of axial velocity corresponding to the fully developed laminar viscous flow is obtained using comsolmultiphysics. In the second stage, the variable-separation method is implemented to reduce the solution of the energy transfer equation under constant wall temperature to an eigenvalue problem. Finally, the temperature distribution is obtained in the analytical form as a series expansion. The influence of fin height on the Nusselt number and the friction factor is discussed.

Modelo de pluma segmento com velocidades estocásticas para dispersão atmosférica em condições de vento fraco

This work presents an analytical solution for the transient three-dimensional advection-diffusion equation. This solution, obtained from a combination of the variable separation method and GILTT (Generalized Integral Laplace Transform Technique) is used to simulate the pollutant dispersion in the atmosphere. The new solution has the advantage of not requiring a numerical inversion performed in the temporal variable in works using only GILTT technique. The model was tested in low wind condition, with diffusion in transverse and longitudinal directions and stochastic speeds. Simulations were performed for the INEL experiment. The analytical character of the model makes it simple, which represents advantages in its development and implementation, as well as in the computational cost for execution.