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It was found that airflow patterns in rooms with cross-ventilation are complex and cannot be predicted by simplified macroscopic models such as the orifice equation.

Generally, the LB-CA method achieves the similar precision with the LES-Lagrangian method, and performs better than some other macroscopic models (such as the two-fluid models).

In this paper, we develop high-order asymptotic preserving (AP) schemes for the BGK equation in a hyperbolic scaling, which leads to the macroscopic models such as the Euler and compressible Navier Stokes equations in the asymptotic limit.

In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the porous media equation, the advection diffusion equation, and the viscous Burgers' equation.

While macroscopic models such as Model 1 are useful first approximations of the dynamics of cumulative cultural evolution, such models have several limitations.

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Many natural processes involve influential smaller scale effects, neglect of which can sometimes cause such macroscopic models to fail to capture important details adequately.

However, in such macroscopic models, component degradations (e.g. cell lysis) are often neglected, even though they can play a significant role.

Currently, because of the efficiency of the macroscopic models, existing structural analysis platforms such as Perform 3D (Computer and Structures Inc. 2006), OpenSEES (PEER 2001), and DRAIN-2DX (Prakash et al. 1993) use macroscopic models for the nonlinear analysis of wall systems.

Theoretical models, such as the sorption isotherm equations, are widely used to simulate the macroscopic competition of metals [16 19].

In such cases, the use of experiments from one microstructure condition to fit macroscopic models may be too limiting.

Such approaches are capable of representing important small-scale phenomena more faithfully than traditional macroscopic models.

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