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Comparison of finite difference and finite volume simulations for a sc-drying mass transport model
2020, Selmer, Ilka, Farrell, Patricio, Smirnova, Irina, Gurikov, Pavel
Different numerical solutions of a previously developed mass transport model for supercritical drying of aerogel particles in a packed bed [Part 1: Selmer et al. 2018, Part 2: Selmer et al. 2019] are compared. Two finite difference discretizations and a finite volume method were used. The finite volume method showed a higher overall accuracy, in the form of lower overall Euclidean norm (l2) and maximum norm (l∞) errors, as well as lower mole balance errors compared to the finite difference methods. Additionally, the finite volume method was more efficient when the condition numbers of the linear systems to be solved were considered. In case of fine grids, the computation time of the finite difference methods was slightly faster but for 16 or fewer nodes the finite volume method was superior. Overall, the finite volume method is preferable for the numerical solution of the described drying model for aerogel particles in a packed bed. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.
Numerical algorithms for Schrödinger equation with artificial boundary conditions
2009, Čiegis, Raimondas, Laukaitytė, Inga, Radziunas, Mindaugas
We consider a one-dimensional linear Schrödinger problem defined on an infinite domain and approximated by the Crank-Nicolson type finite difference scheme. To solve this problem numerically we restrict the computational domain by introducing the reflective, absorbing or transparent artificial boundary conditions. We investigate the conservativity of the discrete scheme with respect to the mass and energy of the solution. Results of computational experiments are presented and the efficiency of different artificial boundary conditions is discussed.