A methodology is presented for the numerical solution of nonlinear elliptic systems in unbounded domains, consisting of three elements. First, the problem is posed on a finite domain by means of a proper nonlinear change of variables. The compressed domain is then discretised, regardless of its final shape, via the radial basis function partition of unity method. Finally, the system of nonlinear algebraic collocation equations is solved with the trust-region algorithm, taking advantage of analytically derived Jacobians. We validate the methodology on a benchmark of computational fluid mechanics: the steady viscous flow past a circular cylinder. The resulting flow characteristics compare very well with the literature. Then, we stress-test the methodology on less smooth obstacles - rounded and sharp square cylinders. As expected, in the latter scenario the solution is polluted by spurious oscillations, owing to the presence of boundary singularities.

翻译：本文提出了一种求解无界域中非线性椭圆系统数值解的方法，包含三个要素。首先，通过适当的非线性变量变换，将问题定义在有限域上。然后，利用径向基函数分区单位法对压缩后的域进行离散化，无论其最终形状如何。最后，采用信赖域算法求解非线性代数配位方程组，并利用解析推导的雅可比矩阵。我们以计算流体力学基准问题——圆柱绕流的稳态粘性流动——验证了该方法。所得的流动特性与文献结果吻合良好。随后，我们在欠光滑障碍物（圆角方形柱和尖角方形柱）上进行了压力测试。如预期般，在后者场景中，由于边界奇异性的存在，解受到了伪震荡的污染。