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A numerical method for the multiphase viscous flow equations

机译:多相粘性流方程的数值方法

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A numerical technique is developed for the solution of the equations that govern multiphase viscous flow. We demonstrate that the equations can be written as a coupled system of Partial Differential Equations (PDEs) comprising: (i) first order hyperbolic PDEs for the volume fraction of each phase; (ii) a generalised Stokes flow for the velocity of each phase; and (iii) elliptic PDEs for the concentration of nutrients and messengers. Furthermore, the computational domain may vary with time for some applications. Appropriate numerical methods are identified for each of these subsystems. The numerical technique developed is then demonstrated using two exemplar applications: tissue engineering; and avascular tumour development. This allows verification that the technique is appropriate for many features of multiphase viscous flow modelling.
机译:为控制多相粘性流的方程式的求解开发了一种数值技术。我们证明了这些方程可以写成偏微分方程(PDE)的耦合系统,该系统包括:(i)每个相的体积分数的一阶双曲PDE; (ii)每个相速度的广义斯托克斯流; (iii)椭圆形偏二苯醚,用于浓缩营养素和信使。此外,对于某些应用,计算域可能会随时间而变化。为这些子系统中的每一个确定了适当的数值方法。然后,使用两个示例应用程序证明了开发的数值技术:组织工程学;组织工程学。和无血管肿瘤的发展。这可以验证该技术适用于多相粘性流建模的许多功能。

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