BACKGROUND The finite volume solver Fluent (Lebanon, NH, USA) is a computational fluid dynamics software employed to analyse biological mass-transport in the vasculature. A principal consideration for computational modelling of blood-side mass-transport is convection-diffusion discretisation scheme selection. Due to numerous discretisation schemes available when developing a mass-transport nume...

The non-orthogonal boundary-fitted coordinate transformation method is applied to the solution of steady three-dimensional momentum and energy equations in laminar flow to obtain temperature field and Nusselt numbers in the thermal entry region of straight ducts of different cross sectional geometries. The conservation equations originally written in Cartesian coordinates are parabolized in the...

A class of higher-order compact upwind biased finite difference (FD) schemes based on the Taylor Series Expansion is developed in this work. The numerical accuracy of this family of compact upwind biased FD schemes is demonstrated by means of Fourier analysis wherein it is shown that these FD schemes have very low dispersion errors over a relatively large bandwidth of wave numbers as compared t...

We report here on our numerical study of the two-dimensional Riemann problem for the compressible Euler equations. Compared with the relatively simple 1-D con gurations, the 2-D case consists of a plethora of geometric wave patterns which pose a computational challenge for highresolution methods. The main feature in the present computations of these 2-D waves is the use of the Riemann-solvers-f...

Abstract We develop flux globalization based well-balanced central-upwind schemes for hydrodynamic equations with general free energy. The proposed are in the sense that they capable of exactly preserving quite complicated steady-state solutions and also capturing traveling waves, even when vacuum regions present. In order to accurately track interfaces near parts solution, we use technique int...

We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development accurate robust numerical methods studied come from complicated wave structures, such as shocks, rarefactions contact discontinuities, arising even smooth initial conditions. In order to reduce diffusion o...

This study examines the effect of discretization schemes for the convection term in the constitutive equation on numerical solutions of viscoelastic fluid flows. For this purpose, a temporally evolving mixing layer, a two-dimensional vortex pair interacting with a wall, and a fully developed turbulent channel flow are selected as test cases, and eight different discretization schemes are consid...