【视频摘要】Detail-preserving smoke simulation using an efficient...

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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.

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