Skip to main content
SpringerLink
Log in

Virtual water wave simulation with multiple wavenumbers

  • Original Article
  • Published:
Virtual Reality Aims and scope Submit manuscript

Abstract

This paper proposes a novel particle-based scheme for simulating interactive water waves. We first modify the implementation of the wave packet so that each packet can carry two wavenumbers. As a consequence, the wavelength-dependent behaviors can be accurately simulated. We then optimize the approximation technique of diffraction for simulating partial diffraction and promoting rendering efficiency. Lastly, we provide a novel evaluation module based on wave patterns generated by solving wave functions. Specifically, we introduce the singular boundary method (SBM) to serve as an analytical solution of the Laplace equation. We tested our scheme and other state-of-the-art approaches on scenes with regular-shaped, complex-shaped, and user-designed obstacles. Various results indicate that, compared to the state of the arts, our scheme can achieve higher physical accuracy and more satisfying computational efficiency.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Bargteil AW, Goktekin TG, O’Brien JF, Strain JA (2006) A semi-Lagrangian contouring method for fluid simulation. ACM Trans Graph 25(1):19–38

    Article  Google Scholar 

  • Bridson R (2015) Fluid simulation for computer graphics. CRC Press

    Book  Google Scholar 

  • Bruno F, Barbieri L, Lagudi A, Cozza M, Cozza A, Peluso R, Muzzupappa M (2018) Virtual dives into the underwater archaeological treasures of South Italy. Virtual Real 22(2):91–102

    Article  Google Scholar 

  • Canabal JA, Miraut D, Thuerey N, Kim T, Portilla J, Otaduy MA (2016) Dispersion kernels for water save simulation. ACM Trans Graph 35(6):1–10

    Article  Google Scholar 

  • Chen W (2009) Singular boundary method: a novel, simple, meshfree, boundary collocation numerical method. Chin J Solid Mech 30(6):592–599

    Google Scholar 

  • Chen W, Fu Z, Wei X (2009) Potential problems by singular boundary method satisfying moment condition. Comput Model Eng 54(1):65–86

    MathSciNet  MATH  Google Scholar 

  • Chentanez N, Müller M (2009) Real-time simulation of large bodies of water with small scale details. In: Proceedings of the ACM SIGGRAPH/Eurographics symposium on computer animation, pp 197–206

  • Da F, Hahn D, Batty C, Wojtan C, Grinspun E (2016) Surface-only liquids. ACM Trans Graph 35(4):1–12

    Article  Google Scholar 

  • Feng G, Liu S (2018) Detail-preserving SPH fluid control with deformation constraint. Comput Animat Virtual Worlds 29(1):1–11

    Article  Google Scholar 

  • Hafner C, Wojtan C (2019) Supplementary material: closed form integration of gravity-capillary rings, pp 1–4

  • Huang K, Ruan J, Zhao Z, Li C, Wang C, Qin H (2019) A general novel parallel framework for SPH-centric algorithms. Proc ACM Comput Graph Interact Tech 2(1):1–16

    Article  Google Scholar 

  • Jiang M, Lan W, Chang J, Dodwell M, Jekins J, Yang HJ, Tong R, Zhang JJ (2018) A game prototype for understanding the safety issues of a lifeboat launch. Virtual Real 22(2):137–148

    Article  Google Scholar 

  • Jensen LS, Golias R (2006) Deep-water animation and rendering. In: Proceedings of the game developer’s conference (Gamasutra), pp 1–13

  • Jeschke S, Skřivan T, Müller-Fischer M, Chentanez N, Macklin M, Wojtan C (2018) Water surface wavelets. ACM Trans Graph 37(4):1–13

    Article  Google Scholar 

  • Jeschke S, Wojtan C (2015) Water wave animation via wavefront parameter interpolation. ACM Trans Graph 34(3):1–14

    Article  MATH  Google Scholar 

  • Jeschke S, Wojtan C (2017) Water wave packets. ACM Trans Graph 36(4):1–12

    Article  MATH  Google Scholar 

  • Kawulich Barbara B, D’Alba Adriana (2019) Teaching qualitative research methods with Second Life, a 3-dimensional online virtual environment. Virtual Real 23(4):375–384

    Article  Google Scholar 

  • Kim D, Song OY, Ko HS (2008) A semi-Lagrangian CIP fluid solver without dimensional splitting. Comput Graph Forum 27(2):467–475

    Article  Google Scholar 

  • Klaseboer E, Manica R, Chan D, Khoo BC (2011) BEM simulations of potential flow with viscous effects as applied to a rising bubble. Eng Anal Bound Elem 35(3):489–494

    Article  MATH  Google Scholar 

  • Lee M, Hyde D, Li K, Fedkiw R (2019) A robust volume conserving method for character-water interaction. In: Proceedings of the ACM SIGGRAPH/Eurographics symposium on computer animation, pp 1–12

  • Liang H, Wu H, Noblesse F (2018) Validation of a global approximation for wave diffraction-radiation in deep water. Appl Ocean Res 74:80–86

    Article  Google Scholar 

  • Liu S, Xiong Y (2013) Fast and stable simulation of virtual water scenes with interactions. Virtual Real 17(1):77–88

    Article  Google Scholar 

  • Loviscach J (2002) A convolution-based algorithm for animated water waves. In: Proceedings of Eurographics (Short Papers), pp. 1-7

  • Mastin GA, Watterberg PA, Mareda JF (1987) Fourier synthesis of ocean scenes. IEEE Comput Graph Appl 7(3):16–23

    Article  Google Scholar 

  • Müller M, Charypar D, Gross M (2003) Particle-based fluid simulation for interactive applications. In: Proceedings of ACM SIGGRAPH/Eurographics symposium on computer animation, pp 154-159

  • Ottosson B (2011) Real-time interactive water waves. Master’s thesis. KTH Royal Institute of Technology

  • Pellas N, Fotaris P, Kazanidis I, Wells D (2019) Augmenting the learning experience in primary and secondary school education: a systematic review of recent trends in augmented reality game-based learning. Virtual Real 23(4):329–346

    Article  Google Scholar 

  • Raveendran K, Wojtan K, Thuerey N, Turk G (2014) Blending liquids. ACM Trans Graph 33(4):1–10

    Article  Google Scholar 

  • Ravnik J, Strelnikova E, Gnitko V, Degtyarev K, Ogorodnyk U (2016) BEM and FEM analysis of fluid-structure interaction in a double tank. Eng Anal Bound Elem 67:13–25

    Article  MathSciNet  MATH  Google Scholar 

  • Razafizana Z, Fu ZJ (2015) Singular boundary method for water wave problems. Ocean Eng 96:330–337

    Article  Google Scholar 

  • Reddy JN (2014) An introduction to nonlinear finite element analysis: with applications to heat transfer, fluid mechanics, and solid mechanics. OUP Oxford

  • Reddy JN, Gartling DK (2010) The finite element method in heat transfer and fluid dynamics. CRC Press

    Book  MATH  Google Scholar 

  • Ren B, Yuan T, Li C, Xu K, Hu SM (2018) Real-time high-fidelity surface flow simulation. IEEE Trans Vis Comput Graph 24(8):2411–2423

    Article  Google Scholar 

  • Schreck C, Hafner C, Wojtan C (2019) Fundamental solutions for water wave animation. ACM Trans Graph 38(4):1–14

    Article  Google Scholar 

  • Skrivan T, Soderstrom A, Johansson J, Sprenger C, Museth K, Wojtan C (2020) Wave curves: simulating Lagrangian water waves on dynamically deforming surfaces. ACM Trans Graph 39(4):1–12

    Article  Google Scholar 

  • Tessendorf J (2001) Simulating ocean water. In: Proceedings of ACM SIGGRAPH courses

  • Tessendorf J (2004) Interactive water surfaces. Game Program Gems 4(8):265–274

    Google Scholar 

  • Tessendorf J (2008) Vertical derivative math for iWave. Clemson University

    Google Scholar 

  • Wu M, Liu S, Xu Q (2021) Improved divergence-free SPH via priority of divergence-free solver and SOR. Comput Animat Virtual Worlds 32(3–4):1–12

    Google Scholar 

  • Wu H, Zhang C, Zhu Y, Li W, Wan D, Noblesse F (2017) A global approximation to the green function for diffraction radiation of water waves. Eur J Mech B Fluids 65:54–64

    Article  MathSciNet  MATH  Google Scholar 

  • Xie C, Jin Y, Liu X (2010) Real-time ocean wave in multi-channel marine simulator. In: Proceedings of ACM SIGGRAPH international conference on virtual reality continuum and its applications in industry, pp 332–335

  • Yang Z, Liu S (2019) An optimization on water wave diffraction approximation based on Wave Packets. Comput Animat Virtual Worlds 30(3–4):1–10

    Google Scholar 

  • Yeh H, Mehra R, Ren Z, Antani L, Manocha D, Lin M (2013) Wave-ray coupling for interactive sound propagation in large complex scenes. ACM Trans Graph 32(6):1–11

    Article  Google Scholar 

  • Yuksel C, House DH, Keyser J (2007) Wave particles. ACM Trans Graph 26(3):1–8

    Article  Google Scholar 

  • Yang Z, Wu M, Liu S (2021) Helmholtz decomposition based SPH. Virtual Real Intell Hardw 3(2):118–128

    Article  Google Scholar 

  • Zhang X, Liu S (2018) Parallel SPH fluid control with dynamic details. Comput Animat Virtual Worlds 29(2):1–14

    Article  Google Scholar 

Download references

Funding

This research was partly supported by the Natural Science Foundation of China under Grant No. 62072328.

Author information

Authors and Affiliations

  1. School of Computer Science and Technology, College of Intelligence and Computing, Tianjin University, Tianjin, 300350, People’s Republic of China

    Shiguang Liu & Zhongyao Yang

Authors
  1. Shiguang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhongyao Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shiguang Liu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, S., Yang, Z. Virtual water wave simulation with multiple wavenumbers. Virtual Reality 27, 1221–1231 (2023). https://doi.org/10.1007/s10055-022-00729-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10055-022-00729-0

Keywords

Search

Navigation