偏微分方程数值计算在虚拟现实中应用与研究

发布时间：2018-03-15 07:14

  本文选题：虚拟现实　切入点：PDE　出处：《舰船科学技术》2017年15期 　论文类型：期刊论文

【摘要】：随着虚拟现实(Virtual Reality,VR)相关硬件的发展以及软件技术的日趋成熟,VR技术正在进入人们的日常生活。然而不可否认,VR的核心问题之一——物理真实感依然没有很好的解决。其原因大多都是由于解算模型控制方程耗费了大量的时间,从而迫使人们采用牺牲精度的方法以满足实时性的要求。而许多的物理模型的解算都归结于偏微分方程求解,因此如何准确高效快速的求解偏微分方程(PDE)和PDE方程组对于提升虚拟现实系统的物理真实感有着至关重要的作用。本文从求解典型PDE出发,建立相应的PDE求解器,并对计算结果进行验证。最后将该思想应用于计算流体力学领域,通过对流体力学中的NS方程和水力学中的浅水波方程的求解,得到计算区域的速度场或高度场,并且对结果进行验证。结果表明,该方法具有较高的可信度。
[Abstract]:With the development of virtual reality (VR) related hardware and the maturation of software technology, VR technology is entering people's daily life. However, there is no denying that one of the core problems of VR, physical reality, has not been solved very well. Most of the reason is that solving the model control equation takes a lot of time, Thus forcing people to use the method of sacrificing precision to meet the requirement of real-time, and many physical models are solved by partial differential equations. Therefore, how to solve PDE (partial differential equation) and PDE equations accurately and efficiently is very important to improve the physical reality of virtual reality system. In this paper, a corresponding PDE solver is established based on the solution of typical PDE. Finally, this idea is applied to the field of computational fluid dynamics. By solving the NS equation and shallow water wave equation in hydrodynamics, the velocity field or height field in the computational region is obtained. The results show that the method is reliable.
【作者单位】： 大连海事大学航海动态仿真和控制实验室;
【基金】：863课题(2015AA016404) 海洋公益性行业科研专项(201505017-4) 中央高校基本科研业务费专项资金资助(3132016310)
【分类号】：O241.82;TP391.9
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本文编号：1614972