In this work we present a new approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common referenced domain: the method relies on a modified set of basis functions and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities. Different mesh motion strategies, based on a Laplacian smoothing technique and on a Radial Basis Function approach, are analyzed and compared. Particular attention is devoted to the role of the non-orthogonal correction. The numerical methods are tested on a heat transfer problem with a parametrized geometry.

中文翻译：

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基于有限体积的降阶方法的有效几何参数化

在这项工作中，我们提出了一种在基于有限体积全阶近似的 POD-Galerkin 降阶方法背景下有效处理参数化几何的新方法。与通常在有限元降阶方法框架中所做的相反，不同的几何图形没有映射到一个共同的参考域：该方法依赖于一组修改过的基函数并利用离散经验插值方法 (D -EIM) 一起处理参数化和非线性的非亲和性。分析和比较了基于拉普拉斯平滑技术和径向基函数方法的不同网格运动策略。特别注意非正交校正的作用。