Adv. Appl. Math. Mech., 9 (2017), pp. 1162-1188.
Published online: 2018-05
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We present a convex-splitting scheme for the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson equation of state for pure substance. The semi-implicit scheme is proven to be uniquely solvable, mass conservative, unconditionally energy stable and $L^∞$ convergent with the order of $\mathcal{O}(∆t+h^2)$. The numerical results verify the effectiveness of the proposed algorithm and also show good agreement of the numerical solution with laboratory experimental results.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0024}, url = {http://global-sci.org/intro/article_detail/aamm/12195.html} }We present a convex-splitting scheme for the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson equation of state for pure substance. The semi-implicit scheme is proven to be uniquely solvable, mass conservative, unconditionally energy stable and $L^∞$ convergent with the order of $\mathcal{O}(∆t+h^2)$. The numerical results verify the effectiveness of the proposed algorithm and also show good agreement of the numerical solution with laboratory experimental results.