A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations
Keyword(s):
Abstract In the paper, a high-order alternating direction implicit (ADI) algorithm is presented to solve problems of unsteady convection and diffusion. The method is fourth- and second-order accurate in space and time, respectively. The resulting matrix at each ADI computation can be obtained by repeatedly solving a penta-diagonal system which produces a computationally cost-effective solver. We prove that the proposed scheme is mass-conserved and unconditionally stable by means of discrete Fourier analysis. Numerical experiments are performed to validate the mass conservation and illustrate that the proposed scheme is accurate and reliable for convection-dominated problems.
2019 ◽
Vol 136
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pp. 139-151
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2014 ◽
pp. 85-115
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2011 ◽
Vol 70
(6)
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pp. 703-712
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2010 ◽
Vol 9
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pp. 1174-1177
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New High-Order Compact ADI Algorithms for 3D Nonlinear Time-Fractional Convection-Diffusion Equation
2013 ◽
Vol 2013
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pp. 1-11
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