Abstract In this paper, we present high order accurate positivity-preserving conservative remapping algorithm which is based on the multi-resolution weighted essentially non-oscillatory (WENO) reconstruction. We use a third-order method on 2D quadrilateral meshes as an example to present the algorithm. The method can effectively remap the physical variables after mesh rezoning in the ALE algorithm. By calculating the intersection exactly, this method does not require the same connectivity between the old and new meshes. By reconstructing a quadratic polynomial and a zero-order polynomial for each cell in a two-dimensional domain, this method assigns nonlinear weights for these polynomials accordingly after calculating the smoothness indicators over the integration area, yielding third order accuracy without numerical oscillations. After calculating the overlaps between the old and new meshes and integrating the polynomials over the intersections, the remapping is completed. Furthermore, to ensure the positivity-preserving property of relevant physical variables in hydrodynamics numerical simulation such as density and internal energy, a simple and efficient positive-preserving limiter is adopted to slightly modify the reconstructed polynomials, which can maintain the original order of accuracy and conservation. The algorithm can be extended to higher order accuracy using higher order reconstruction and higher order integration formula over the intersection areas. A series of numerical experiments are performed to test the properties of the multi-resolution WENO conservative remapping algorithm. Numerical results show that the algorithm is conservative, positivity-preserving, highly efficient, third-order accurate for smooth problems, and essentially non-oscillatory for discontinuous problems.

中文翻译：

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二维四边形网格上的高阶保正性保守WENO重映射方法

摘要 在本文中，我们提出了基于多分辨率加权本质非振荡（WENO）重建的高阶精确正性保留保守重映射算法。我们以二维四边形网格上的三阶方法为例来介绍该算法。该方法可以有效地重新映射ALE算法中网格重分区后的物理变量。通过精确计算交点，该方法不需要新旧网格之间具有相同的连接性。通过在二维域中为每个单元重建二次多项式和零阶多项式，该方法在计算积分区域上的平滑度指标后，相应地为这些多项式分配非线性权重，产生三阶精度而没有数值振荡。在计算新旧网格之间的重叠并在交叉点上对多项式进行积分后，重新映射就完成了。此外，为了保证密度、内能等流体动力学数值模拟中相关物理变量的保正性，采用简单高效的保正限幅器对重构的多项式进行微修改，保持原有的精度和保护。使用交叉区域上的高阶重建和高阶积分公式，该算法可以扩展到更高阶的精度。进行了一系列数值实验以测试多分辨率WENO保守重映射算法的性质。数值结果表明该算法是保守的，