We provide a method to compute the entropy-satisfying weak solution to the eikonal equation in an arbitrary-order polynomial space. The method uses an artificial viscosity approach and is demonstrated for the signed distance function, where exact solutions are available. The method is designed specifically for an existing high-order discontinuous-Galerkin framework, which uses standard convection, diffusion, and source terms. We show design order of accuracy and good behavior for both shocks and rarefaction type solutions. Finally the distance function around a complex multi-element airfoil is computed using a high-order-accurate representation.
翻译:我们提供了一种方法,用来计算任意顺序多元空间中电离方程式的电离子满足性弱溶液。该方法使用人工粘度法,并在有精确溶液的情况下用于签名的距离函数。该方法专门设计为现有的高顺序不连续-伽勒金框架,该框架使用标准对流、扩散和源术语。我们显示了震荡和稀有动作型解决方案的准确性和良好行为设计顺序。最后,使用高顺序-准确度代表法计算复杂的多元素空气浮油周围的距离功能。