Real-time water wave simulation method based on wave annulus particles

doi:10.11772/j.issn.1001-9081.2021091700

Abstract

Abstract:

A real-time two-dimensional water wave simulation method based on wave annulus particle packet was proposed to reduce computational cost in the water wave simulation process and improve its diffusion phenomenon's fidelity. In this method， wave annulus particle was used as primary calculation unit， the concept of “wave packet” was inherited inside particles， and visual effect of water waves was reproduced by using superposition of water waves in multiple frequency bands. Collision calculation was reduced by adding a mirror wave source to avoid complex geometric judgment when calculating the water wave reflection process. Additional calculation accuracy parameters were provided so that the algorithm could adjust calculation complexity of water wave reflection according to different hardware calculation capabilities. Experimental results show that the proposed method can use fewer particles to simulate natural water wave motion and avoid problem of water wave fracture after collision reflection. The performance test on the same hardware platform shows that rendering frame rate of the proposed wave annulus simulation algorithm is at least 60% higher than that of traditional wave packet algorithm and even achieves an acceleration effect of more than 400% in some cases with particularly complex water wave states.

Key words: water wave simulation, wave annulus particle, wave packet, particle system, rendering frame rate

摘要：

为了降低水波模拟过程中的计算成本并提高其扩散现象的逼真度，提出一种基于波环粒子包的实时二维平面水波仿真方法。该方法采用波环粒子为基本计算单元，粒子内部继承“波包”的概念，使用多个频段水波叠加的方式再现水波视觉效果。在计算水波反射过程时，通过添加镜像波源的形式减少碰撞计算，避免复杂几何判定。为适应不同硬件的计算性能差异，该方法提供额外的计算精度参数，可针对不同硬件计算能力调节水波反射计算复杂度。实验结果表明，该方法可使用较少的粒子模拟出较为真实的水波运动，且避免了碰撞反射后水波断裂的问题。在相同硬件平台上的性能测试显示，所提波环仿真方法的渲染帧率比传统波包算法高出至少60%，在一些水波状态特别复杂的情况下可达到400%以上的加速效果。

关键词: 水波仿真, 波环粒子, 波包, 粒子系统, 渲染帧率

CLC Number:

TP391.9

Haojie GU, Jun ZHANG. Real-time water wave simulation method based on wave annulus particles[J]. Journal of Computer Applications, 2022, 42(12): 3876-3883.

顾浩杰, 张军. 基于波环粒子的实时水波仿真方法[J]. 《计算机应用》唯一官方网站, 2022, 42(12): 3876-3883.

Figures/Tables 23

Fig.1 Accumulation phenomenon of small particles

Fig. 2 Comparison of rectangular particle and wave annulus particle in simulating water waves

Fig. 3 Framework of the proposed algorithm

Fig. 4 Multiband one-dimensional wave function stacking

Fig.5 Multiband band wave annulus particles stacking

Fig. 6 Update of boundary dynamic table

Fig. 7 Implementations flow of the proposed algorithm

Fig. 8 Height calculation of water surface grid

Fig. 9 Simulation of single wave source without dispersion

Fig. 10 Simulation of single wave source with dispersion

Tab. 1 Radius variation of wave annulus particles

粒子ID	波源ID	时间步长
粒子ID	波源ID	100	200	300	400
1	1	5.867 3	9.989 5	14.374 5	18.524 1
2	1	5.510 6	8.912 1	12.515 8	15.919 9
3	1	5.819 6	9.546 3	13.501 1	17.242 1
4	1	—	8.694 1	12.046 7	15.212 6
5	2	—	—	4.464 7	8.683 4

Tab. 2 Union of boundary dynamic tables

波源ID	边界ID
波源ID	1	2	3	4	5
1	39.830 0	33.074 9	31.945 0	47.457 5	60.170 0
2	55.253 4	40.122 1	26.487 8	32.692 6	44.746 6

Fig. 11 Collision simulation of the proposed method

Tab. 3 Comparison of amplitudes of single particles with different damping

阻尼项	时间步长
阻尼项	100	200	300	400	500
无阻尼	0.133 2	0.099 7	0.083 2	0.072 8	0.065 5
$ξ = 1$	0.119 0	0.079 6	0.059 2	0.046 3	0.037 2
$ξ = 2$	0.106 4	0.063 5	0.042 2	0.029 4	0.021 1
$ξ = 3.5$	0.089 9	0.045 2	0.025 3	0.014 9	0.009 0

Tab. 3 Comparison of amplitudes of single particles with different damping

阻尼项	时间步长
阻尼项	100	200	300	400	500
无阻尼	0.133 2	0.099 7	0.083 2	0.072 8	0.065 5
$ξ = 1$	0.119 0	0.079 6	0.059 2	0.046 3	0.037 2
$ξ = 2$	0.106 4	0.063 5	0.042 2	0.029 4	0.021 1
$ξ = 3.5$	0.089 9	0.045 2	0.025 3	0.014 9	0.009 0

Fig. 12 Wave diffusion without damping

Fig. 13 Wave diffusion of proposed method

Fig. 14 Comparison of number of particles required for water wave simulation

Fig. 15 Comparison of water wave collision reflection effect

Fig. 16 Comparison of raindrop ripple simulation effect

Fig.17 Comparison of calculation time of single wave source on CPU

Fig.18 Comparison of single wave simulation FPS in complex environment

Tab.4 Comparison of multi-wave source simulation FPS in complex environment

时间步长	1个波源		2个波源		3个波源		4个波源
时间步长	本文方法	文献［11］方法	本文方法	文献［11］方法	本文方法	文献［11］方法	本文方法	文献［11］方法
1 000	115.281	75.728	100.016	61.188	87.093	55.512	72.631	45.587
2 000	73.937	38.818	51.208	24.007	42.175	16.114	31.627	11.240
3 000	69.776	19.242	42.959	10.064	39.719	7.151	31.919	5.150
4 000	108.902	25.742	82.555	14.876	77.383	10.632	69.067	8.254
5 000	156.128	58.595	157.678	44.594	155.847	36.675	155.463	27.642

Fig.19 Simulation of multi-wave source water wave in pool scene

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