Detail-preserving smoke simulation using an efficient high-order numerical scheme

Zhu, Jian; Yang, Zhuo; Sun, Hao; Wu, Enhua; Cai, Ruichu; Zhang, Hao

doi:10.1007/s11432-018-9889-8

Cited by 1 publication

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For high‐dimensional applications, for example, 3D fluid simulation, the computation is too large and the memory consumption is too high. Fukumitsu et al 14 proposed to use local Taylor expansion to approximate high‐order derivatives in dimensional splitting based CIP (DSCIP) with low memory cost, in this article we first use our previous work, 22 which is similar to Fukumitsu et al's work but with higher stability, to construct a 2D CIP‐based advection, and then define an efficient way to extend it to 3D.…”

Section: Cip Methods In 1dmentioning

confidence: 99%

“…As a result, only

ϕ

and its first‐order derivatives

[\partial_{x} ϕ, \partial_{y} ϕ]

are stored on grid as computational variables, thus saving memory overheads. Similar to their method, we also use Taylor expansion to approximate the high‐order derivatives, 22 but our method is more stable and more suitable for expansion to higher dimensions.…”

Section: Our Methodsmentioning

confidence: 99%

“…Some work attempted to fix this problem, for example, by not applying derivative constraints to each grid point, 13 and by using finite difference to approximate high‐order derivatives, 11 but paid corresponding prices, for example, reduced accuracy or causing instability. Fukumitsu et al 14 proposed a dimensional splitting CIP scheme with low memory cost, but the scheme may cause instability, we simulated detailed smoke using a similar idea with high stability, 22 but it is only applicable for 2D simulations.…”

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Animating turbulent fluid with a robust and efficient high‐order advection method

Zhu

Cai

et al. 2020

Computer Animation & Virtual

Self Cite

View full text Add to dashboard Cite

The accuracy of advection has a great influence on the visual effect of fluid simulation. Constrained interpolation profile (CIP) method has been an important advection scheme because of its third-order accuracy and the fact that it only needs to be performed over a compact stencil, but extending it to high-dimensional advection equations is not easy, because it involves complex calculations and large memory overheads, and is usually unstable. In this article, we propose a stable and efficient three-dimensional (3D) CIP scheme which can maintain high accuracy but requires low computation and memory cost. We first construct an efficient two-dimensional (2D) CIP scheme based on dimensional splitting and local Taylor expansions, and then propose an effective way to extend it for 3D applications without decreasing the computational accuracy or affecting the stability. The experimental results show the advantages of our method over the state-of-the-art advection schemes. K E Y W O R D S constrained interpolation profile, fluid simulation, high-order advection, Taylor expansion 1 INTRODUCTION Various kinds of methods 1 have been proposed to solve the advection step in Eulerian fluid simulation, but most of them can only reach the second-order accuracy, such as back and forth error compensation and correction (BFECC) 2,3 and MacCormack, 4 and so forth. The advection methods with higher order accuracy usually need to be performed over a wide stencil, such as the essentially nonoscillatory (ENO) 5 and weighted ENO (WENO) 5 methods, which results in a large amount of calculation and cannot be extended to nonuniform grids.

show abstract

Section: Cip Methods In 1dmentioning

confidence: 99%

“…As a result, only