scholarly journals Natural Convection Numeric Simulation on Metal Freezing Using Differential Method

2017 ◽  
Vol 16 (2) ◽  
Author(s):  
Heri Suprianto ◽  
Eko Prasetyo Budiana ◽  
Purwadi Joko Widodo
Keyword(s):  
Fluid Flow ◽  
Natural Convection ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Governing Equation ◽  
Solidification Process ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Flow Profile ◽  
Metal Solidification

The research of modeling of natural convection in metal solidification process with finite different method was conducted to determine temperature distribution and fluid flow profil with variations value Rayleigh number. The research conducted by solving governing equation of natural convection with finite difference approximation. Governing equation of natural convection consist of continuity equation, momentum equations, and energy equation. The ADI (Alternating Directional Implicit) method was used to discriteze for governing equation of natural convection. Finite difference method was written in Fortran language whereas the temperature distribution and fluid flow profile were visualized with Matlab software. The results of this research was validated by comparing the results obtained with Rajiv Sampath research. Comparison of the results of research showed good agreement. The result showed that solidification process occurs faster at Ra 10^4 compared with 10^5 and 10^6

Finite-Difference Approximation for Fluid-Flow Simulation and Calculation of Permeability in Porous Media

2012 ◽  
Vol 94 (3) ◽  
pp. 775-793 ◽  
Author(s):  
Vahid Shabro ◽  
Carlos Torres-Verdín ◽  
Farzam Javadpour ◽  
Kamy Sepehrnoori
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Finite Difference ◽  
Flow Simulation ◽  
Finite Difference Approximation ◽  
Difference Approximation

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

A parameter-uniform finite difference scheme for singularly perturbed parabolic problem with two small parameters

2021 ◽  
Author(s):  
Tesfaye Aga Bullo ◽  
Guy Aymard Degla ◽  
Gemechis File Duressa
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Variable Parameter ◽  
Accurate Solution ◽  
Singularly Perturbed ◽  
Finite Difference Approximation ◽  
Parabolic Problems ◽  
Difference Approximation ◽  
Uniform Mesh

A parameter-uniform finite difference scheme is constructed and analyzed for solving singularly perturbed parabolic problems with two parameters. The solution involves boundary layers at both the left and right ends of the solution domain. A numerical algorithm is formulated based on uniform mesh finite difference approximation for time variable and appropriate piecewise uniform mesh for the spatial variable. Parameter-uniform error bounds are established for both theoretical and experimental results and observed that the scheme is second-order convergent. Furthermore, the present method produces a more accurate solution than some methods existing in the literature.   

Sign in / Sign up

Export Citation Format

Share Document