FOURTH-ORDER ACCURATE FINITE DIFFERENCE SOLUTION OF THE TRANSIENT HEAT TRANSFER EQUATION
Keywords:
High-order compact finite difference scheme, Transient Diffusion, heat equationAbstract
In this paper a high-order compact solution is presented for the transient diffusion equation
subject to both homogeneous as well as insulated boundary conditions. The finite difference
scheme is fourth order accurate both in space and time. The central difference scheme is used to approximate the space derivatives. The higher order terms in 'the Taylor series expansion are approximated using the governing differential equations. The difference equations are integrated by applying a Runge-Kutta scheme. Numerical results are compared with exact solutions.
References
Leonard, B. P., 1979, "A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation", Computer Methods in Applied Mechanics and Engineering, vol. 19, pp. 59-98.
Bradley, D., Missaghi, M., and Chin, S. R, 1988, "A Taylor Series Approach to Numerical Accuracy and a Third-Order Scheme for Strong Convective Flows", Computer Methods in Applied Mechanics and Engineering, vol. 69, pp. 133-151.
Gupta Datta, A., Lake, L.W., Pope, G.A., and Sepehrnoori, K., 1991, "High Resolution Monotonic Schemes for Reservoir Fluid Flow Simulation", In Situ, vol. 15, part 3, pp. 289-317.
Harten, A., Engquist, B., Osher, S., and Chakravarthy, S. R., 1987, "Uniformly High Order Accurate Essentially Non-Oscillatory Schemes If', Journal of Computational Physics, vol. 83, pp. 231-303.
Harten, A., Engquist, B., Osher, S., and Chakravarthy, S. R., 1987, "Uniformly High Orfer Essentially Non-Oscillatory Schemes III', Journal of Computational Physics, vol. 83, part 2, pp. 231-303.
Jain, M. K., Jain, R. K., and Mohanty, R. K., 1992, "Fourth-Order Finite Difference Methods for Three Dimensional Elliptic Equations with NonLinear First-Derivative Terms", Numerical Methods for Partial Differential Equations, vol. 8, part 6, pp. 575-591.
Lele, S. K., 1992, "Compact Finite Difference Schemes with Spectral-Like Resolution", Journal of Computational Physics, vol. 103, pp. 16-42.
Hirsh, R. S., 1975, "Higher Order Accurate Difference Solution of Fluid Mechanics Problems by a Compact Differencing Technique", Journal of Computational Physics, vol. 9, part 1, pp. 90-109.
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