An Efficient Multi-Scale Modelling Approach for ssDNA Motion in Fluid Flow

The paper presents a multi-scale modelling approach for simulating macromolecules in fluid flows. Macromolecule transport at low number densities is frequently encountered in biomedical devices, such as separators, detection and analysis systems. Accurate modelling of this process is challenging due to the wide range of physical scales involved. The continuum approach is not valid for low solute concentrations, but the large timescales of the fluid flow make purely molecular simulations prohibitively expensive. A promising multi-scale modelling strategy is provided by the meta-modelling approach considered in this paper. Meta-models are based on the coupled solution of fluid flow equations and equations of motion for a simplified mechanical model of macromolecules. The approach enables simulation of individual macromolecules at macroscopic time scales. Meta-models often rely on particle-corrector algorithms, which impose length constraints on the mechanical model. Lack of robustness of the particle-corrector algorithm employed can lead to slow convergence and numerical instability. A new FAst Linear COrrector （FALCO） algorithm is introduced in this paper, which significantly improves computational efficiency in comparison with the widely used SHAKE algorithm. Validation of the new particle corrector against a simple analytic solution is performed and improved convergence is demonstrated for ssDNA motion in a lid-driven micro-cavity.

A Unified Fractional-Step,Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

This paper introduces a unified concept and algorithm for the fractionalstep(FS),artificial compressibility(AC)and pressure-projection(PP)methods for solving the incompressible Navier-Stokes equations.The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based(CB)Godunov-type treatment of convective terms with PP methods.Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP(split)methods,thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible.Therefore,the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a)overcome the numerical stiffness of the classical AC approach at(very)low and moderate Reynolds numbers,b)incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods,and c)further improve the stability and efficiency of the AC method for steady and unsteady flow problems.The FSAC-PP method has also been coupled with a non-linear,full-multigrid and fullapproximation storage(FMG-FAS)technique to further increase the efficiency of the solution.For validating the proposed FSAC-PP method,computational examples are presented for benchmark problems.The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems.

Implicit Unstructured-Mesh Method for Calculating Poiseuille Flows of Rarefied Gas

An implicit high-order accurate method for solving model kinetic equations is proposed.The method is an extension of earlier work on the construction of an explicit TVD method for hybrid unstructured meshes in physical space and is illustrated on the Poiseuille flow of rarefied gas.Examples of calculations are provided for different Knudsen numbers and mesh resolutions,which illustrate the efficiency and high accuracy of the new scheme.

WENO Schemes for Mixed-Element Unstructured Meshes

The paper extends weighted essentially non-oscillatory(WENO)schemes to two-dimensional quadrilateral and mixed-element unstructured meshes.The key element of the proposed methods is a reconstruction procedure suitable for arbitrarilyshaped cells.The resulting schemes achieve the designed uniformly high-order of accuracy and compute discontinuous solutions without spurious oscillations at interfaces between cells of two different types.