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首页> 外文期刊>Journal of Computational Physics >A matched interface and boundary method for solving multi-flow Navier-Stokes equations with applications to geodynamics
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A matched interface and boundary method for solving multi-flow Navier-Stokes equations with applications to geodynamics

机译：求解多流Navier-Stokes方程的接口和边界匹配方法及其在地球动力学中的应用

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摘要

We have developed a second-order numerical method, based on the matched interface and boundary (MIB) approach, to solve the Navier-Stokes equations with discontinuous viscosity and density on non-staggered Cartesian grids. We have derived for the first time the interface conditions for the intermediate velocity field and the pressure potential function that are introduced in the projection method. Differentiation of the velocity components on stencils across the interface is aided by the coupled fictitious velocity values, whose representations are solved by using the coupled velocity interface conditions. These fictitious values and the non-staggered grid allow a convenient and accurate approximation of the pressure and potential jump conditions. A compact finite difference method was adopted to explicitly compute the pressure derivatives at regular nodes to avoid the pressure-velocity decoupling. Numerical experiments verified the desired accuracy of the numerical method. Applications to geophysical problems demonstrated that the sharp pressure jumps on the clast-Newtonian matrix are accurately captured for various shear conditions, moderate viscosity contrasts and a wide range of density contrasts. We showed that large transfer errors will be introduced to the jumps of the pressure and the potential function in case of a large absolute difference of the viscosity across the interface; these errors will cause simulations to become unstable.
机译：我们已经开发了一种基于匹配界面和边界（MIB）方法的二阶数值方法，用于在非交错笛卡尔网格上求解具有不连续粘度和密度的Navier-Stokes方程。我们首次导出了投影方法中引入的中间速度场和压力势函数的界面条件。通过耦合的虚拟速度值可以帮助区分模板上的模板上的速度分量，通过使用耦合的速度接口条件可以解决其表示。这些虚拟值和不交错的网格使压力和可能的跳跃条件变得方便而准确。采用紧凑的有限差分法来显式计算规则节点处的压力导数，以避免压力-速度解耦。数值实验验证了数值方法的期望精度。在地球物理问题上的应用表明，对于各种剪切条件，适度的粘度对比和宽范围的密度对比，克拉斯特-牛顿矩阵上的急剧压力跳跃都可以准确捕获。我们发现，如果界面上的粘度绝对差较大，则传递误差会引入压力和势函数的跃迁;这些错误将导致仿真变得不稳定。

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