更多精彩视频登陆网站

www.koushare.com

The advection step in Eulerian fluid simulation is prone to numerical dissipation, resulting in the loss of fluid details. Among the various attempts to develop accurate advection solvers, high-order advection schemes such as back and forth error compensation and correction (BFECC) and MacCormack are effective solutions. Complementary to high-order advection schemes are high-order interpolation schemes such as monotonic cubic spline in the graphics field and essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes in computational fluid dynamics. However, these schemes are computed over wide stencils, incurring a significant algorithm complexity cost and potential problems on nonuniformly spaced grids.

The constrained interpolation profile (CIP) method constructs an interpolation function in only one mesh cell, achieving desirable thirdorder accuracy on a compact stencil. Despite these advantages over other advection schemes, it is not easy to extend CIP to higher dimensions due to the computational complexity and high memory cost. This problem is only partially solved by current multi-dimensional CIP-based advection solvers, such as monotonic CIP (MCIP) and unsplit semi-Lagrangian CIP (USCIP). Moreover, these algorithms may cause other problems such as decreased accuracy or instability. Developing an efficient high-dimensional CIP scheme that retains high accuracy remains a challenging problem.

Herein, we propose an efficient CIP scheme based on directional splitting. Unlike the existing CIP-based schemes, in which high-order derivatives are usually treated as unknowns to ensure high accuracy, the resulting scheme takes only the physical quantity and its first-order derivatives as unknown variables and approximates the highorder derivatives with third-order accuracy using local Taylor expansions. The proposed method considerably reduces the time and memory overhead without impairing the numerical accuracy; thus, it efficiently reproduces the rich fluid details.

......

点击下方“阅读原文”，更有料!

蔻享科学平台秉承传播科学、共享科学、服务科学的理念，为广大科研工作者呈现最新科研动态。有发表的最新成果，大家可以录制视频摘要（时长不超过10分钟）发送至蔻享，蔻享免费为大家宣传。欢迎投稿！

◆【视频摘要】人工智能预测蛋白质“光学指纹”

◆【视频摘要】半经典动力学和非线性电流

◆【视频摘要】基于零空间超构材料的变换光学器件及其弱化实现方案

◆【视频摘要】亚波长波导模式转换的瞬态过程研究：光学芯片中模式转换和太赫兹集成器件的新思路

◆【科学综述】硼烯及其在能源与催化领域的研究进展

◆【科学综述】Local electrical characterization of two-dimensional materials with functional atomic force microscopy

◆【科学综述】The rise of two-dimensional MoS2 for catalysis