One-dimensional linear advection-diffusion equation: Analytical and finite ele- ment solutions. Computers Fluids, 107:189 - 195, 2015.A. Mojtabi and M. O. Deville, "One-dimensional linear advection-diffusion eq
We present an analytical form for the effective coefficient to linear diffusion equations such that the heterogeneous coefficients are periodic and rapidly oscillating and can be defined as step functions describing inclusions in a main matrix. The new contribution comes from using an analytical approxima...
in which the homogeneous solution reads as: (39) (40)with the coefficients and related to local dispersion and mean advection: (41) (42) Substituting Equation 37 into itself creates a series expansion of the concentration field which is the centerpiece in the approach of Dentz et al. (...
In this section, we present numerical results for two representative examples, a diffusion–advection–reactionequation and a high-dimensional (dissipative) Rosen–Zener model. In particular, we illustrate the behaviour of the novel schemes CF4[4],CF5[4],CF3[5],CF4[6],CF5[6],CF5C[6],comp...
It should be noted that the velocity v only describes the velocity of the defect density ρ and is not, in general, the same as the advection velocity of the order parameter. We have only shown that if ρ ≠ 0 in some region then it is possible to write the evolution of Ψ in...
1In a physical model, the derived quantity of interest is obtained by applying the constitutive law to the given parameters and unknown state, and then is verified and updated by checking whether it satisfies the governing equation. Hong et al. Advanced Modeling and Simulation in Engineering ...
equilibrium_x: -sigma_xx__x - sigma_xy__yequilibrium_y: -sigma_xy__x - sigma_yy__ytraction_x: normal_x*sigma_xx + normal_y*sigma_xytraction_y: normal_x*sigma_xy + normal_y*sigma_yy"""name="LinearElasticity"def__init__(self,E=None,nu=None,lambda_=None,mu=None,rho=1...
The fundamental solution of the space–time fractional advection-dispersion equation J. Appl. Math. Comput., 18 (1–2) (2005), pp. 339-350, 10.1007/BF02936577 View in ScopusGoogle Scholar Le Mẽhautẽ and Crepy, 1983 A. Le Mẽhautẽ, G. Crepy Introduction to transfer and motion...
(VPM) is unstable by itself because it does not conserve the total amount of circulation as time evolves (Kelvin's circulation theorem), an isolated Vortex (regular‑ ized) Filament Method (VFM) approach is implemented to obtain advection of vorti‑ city, while ...
The class of problems described by (1) comprises, among others, the advection equation, the acoustic or elastic wave equations, and the Maxwell equations, cf., [2, 3, 5, 29]. In this paper, we employ the framework of (abstract) evolution equations. This allows us to study the well...