We formulate an oversampled radial basis function generated finite difference (RBF-FD) method to solve time-dependent nonlinear conservation laws. The analytic solutions of these problems are known to be discontinuous, which leads to occurrence of non-physical oscillations (Gibbs phenomenon) that pollute the numerical solutions and can make them unstable. We address these difficulties using a residual based artificial viscosity stabilization, where the residual of the conservation law indicates the approximate location of the shocks. The location is then used to locally apply an upwind viscosity term, which stabilizes the Gibbs phenomenon and does not smear the solution away from the shocks. The proposed method is numerically tested and proves to be robust and accurate when solving scalar conservation laws and systems of conservation laws, such as compressible Euler equations.

翻译：我们制定了过度抽样的辐射基函数,从而产生有限的差异(RBF-FD)方法,解决时间依赖的非线性养护法。这些问题的分析性解决办法已知是不连续的,导致非物理振荡(Gibbs 现象)的发生,从而污染了数字解决方案并可能使其不稳定。我们利用基于残留的人工防腐度稳定办法来解决这些困难,其中保存法的剩余部分表明这些冲击的大致位置。然后,该地点用于在当地应用一个上风的粘度术语,该术语稳定了Gibbs现象,并且不会抹除震荡的解决方案。 拟议的方法经过数字测试,在解决可压缩的 Euler 方程式等质量养护法和养护法体系时证明是稳健和准确的。