An Efficient Formulation of the Modified Nodal Integral Method and Application to the Two-Dimensional Burgers' Equation
- University of Illinois at Urbana-Champaign (United States)
An alternate formulation of the recently proposed modified nodal integral method (MNIM) has been developed to further reduce computation time when solving nonlinear partial differential equations with a nonlinear convection term such as Burgers' equation and the Navier-Stokes equation. In this formulation, by adding and subtracting a linearized convection term, in which the node-averaged velocity at the previous time step multiplies the spatial derivative, the node-interior approximate analytical solution is developed in terms of this previous time-step node-averaged velocity. This leads to a set of discrete equations with coefficients that need to be evaluated only once each time step for each node, resulting in a significant reduction in computing time when compared with the original MNIM formulation. A numerical scheme using the node-averaged velocities at the previous time step - to be referred to as M{sup 2}NIM - for the two-dimensional, time-dependent Burgers' equation has been developed. The method is shown to be second order and to posses inherent upwinding. When compared with MNIM, numerical results show a significant reduction in the computation time without sacrificing accuracy.
- OSTI ID:
- 20804750
- Journal Information:
- Nuclear Science and Engineering, Vol. 139, Issue 3; Other Information: Copyright (c) 2006 American Nuclear Society (ANS), United States, All rights reserved. http://epubs.ans.org/; Country of input: International Atomic Energy Agency (IAEA); ISSN 0029-5639
- Country of Publication:
- United States
- Language:
- English
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