SBIR Phase I: Highly Accurate Reconstruction Module For Multidisciplinary Computation

这个小企业创新研究第一阶段项目将开发一个高精度的重建模块Godunov型计划，以提升当前多学科计算软件包的能力，用于模拟一类小规模和高频率的工程问题。这项工作的独特和创新的方面是联合收割机结合加权基本无振荡（韦诺）的概念和紧凑的差分到一个单一的迎风算法。 而不是使用多个多项式候选人，混合幂指数样条被用来作为潜在的插值的韦诺计划与当地的光滑措施作为扰动参数。通过这种方式，韦诺方案的权函数可以从底层插值解析地确定。 它们在光滑区域周围的泰勒级数展开可用于进一步提高精度。由此产生的分段二次重建与紧凑的差异计算的斜率和曲率，可以显着减少数值扩散固有的迎风格式。利用这种迎风格式，可以对涡控流动、边界层、湍流、声波和电磁波等进行数值模拟，可以在不损失冲击捕获特征的情况下得到显著改善。 高度精确的重建模块，这是独立的物理，可以很容易地集成到当前的生产和研究代码，并提供了至少一个数量级的成本改进的潜力，在目前的版本。

This Small Business Innovation Research Phase I project will develop a highly accurate reconstruction module for Godunov-type schemes to upgrade the capability of current multidisciplinary computational software packages for simulation of a class of engineering problems with small scales and high frequencies. The unique and innovative aspect of this work is to combine both Weighted Essentially Non-Oscillatory (WENO) concept and compact differencing into a single upwind algorithm. Instead of using multiple polynomial candidates, a hybrid power-exponential spline is used as the underlying interpolation for a WENO scheme with local smoothness measures as the perturbation parameters. In this way, the weight functions of a WENO scheme can be analytically determined from the underlying interpolation. Their Taylor series expansions around the smooth regions can be used for further accuracy improvement. The resulting piecewise quadratic reconstruction with compact difference computed slope and curvature can dramatically reduce numerical diffusion inherent in upwind schemes. By using this upwind scheme, the numerical simulation of vortex dominated flows, boundary layers, turbulence, acoustic waves, and electromagnetic waves, etc., can be significantly improved without loss of the shock-capturing feature. The highly accurate reconstruction module, which is independent of physics, can be easily integrated into the current production and research codes and has the potential of providing cost improvement of at least an order of magnitude over the current versions.