A Finite Difference Scheme for the Heat Conduction Equation
نویسندگان
چکیده
We use equations similar to the heat conduction equation to calulate heat transfer, radiation transfer and hydrostatical equilibrium in our stellar evolution programs. We tried various numerical schemes and found that the most convenient scheme for complicated calculations (nonlinear, multidimensional calculations) is a symmetrical semi-implicit (SSI) scheme. The (SSI) scheme is easy to code, very economical in computer time and in computer fast memory, and at the same time it is unconditionally stable and quite accurate.
منابع مشابه
Analytical Analysis of The Dual-phase-lag Heat Transfer Equation in a Finite Slab with Periodic Surface Heat Flux (RESEARCH NOTE)
This work uses the dual-phase-lag (DPL) model of heat conduction to demonstrate the effect of temperature gradient relaxation time on the result of non-Fourier hyperbolic conduction in a finite slab subjected to a periodic thermal disturbance. DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. For the ...
متن کاملMoving Mesh Non-standard Finite Difference Method for Non-linear Heat Transfer in a Thin Finite Rod
In this paper, a moving mesh technique and a non-standard finite difference method are combined, and a moving mesh non-standard finite difference (MMNSFD) method is developed to solve an initial boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. In this method, the moving spatial grid is obtained by a simple geometric adaptive algorithm ...
متن کاملA Numerical Study of Natural Convection and Radiation Interaction in Vertical Circular Pin
A numerical finite difference study has been earned out for two dimensional radiation-natural convection interaction phenomena in a vertical circular pin located at a non-participating (i.e. transparent) fluid. The coupled conservation equations in boundary layer (continuity, momentum, and energy equations) and pin energy equation are solved simultaneously using modified box method and fully im...
متن کاملHybrid differential transform-finite difference solution of 2D transient nonlinear annular fin equation
In the present paper, hybrid differential transform and finite difference method (HDTFD) is applied to solve 2D transient nonlinear straight annular fin equation. For the case of linear heat transfer the results are verified with analytical solution. The effect of different parameters on fin temperature distribution is investigated. Effect of time interval of differential transform on the stabi...
متن کاملA novel computational procedure based on league championship algorithm for solving an inverse heat conduction problem
Inverse heat conduction problems, which are one of the most important groups of problems, are often ill-posed and complicated problems, and their optimization process has lots of local extrema. This paper provides a novel computational procedure based on finite differences method and league championship algorithm to solve a one-dimensional inverse heat conduction problem. At the beginning, we u...
متن کامل