偏微分方程数值计算在虚拟现实中应用与研究

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.

Application and research of numerical calculation of partial differential equations in virtual reality

With the development of virtual reality hardware and software, VR technology is entering people's daily life. However, there is no denying that the core issue of VR-physical reality does not have a good solution. Mostly it is because of the complexity of control equation which takes a lot of time to solve; hence it forces people to adopt alternative method of sacrificing precision to meet the real-time requirements. Whereas many of the physical models of the solution are attributed to solving partial differential equations, so how to accurately and efficiently solve partial differential equation (PDE) and PDEs has a crucial role in enhancing VR-physical sense in the virtual reality system. Based on the solution of typical PDE, the corresponding PDE solver is established and the calculation results are verified. Finally, the method is applied in the field of computational fluid dynamics, the solution of shallow water wave equation of the fluid mechanics in the NS equations and hydraulics, the velocity field in the area or height field are calculated and validated. The results show that the method has high reliability.