When solving CFD problems, the solver, or the numerical code, plays an important role. Depending on the phenomena and problem domain, designing such numerical codes can be hard work. One strategy is to start with simple problems and construct the code as building blocks. The purpose of this work is to provide a detailed review of the theory to compute analytical and exact solutions, and recent numerical methods to construct a code to solve compressible and inviscid fluid flows with high-resolution, arbitrary domains, non-linear phenomena, and on rectangular meshes. We also propose a modification to the inverse Lax–Wendroff procedure solid wall treatment and two-dimensional WENO-type extrapolation stencil selection and weights to handle more generic situations. To test our modifications, we use the finite difference method, Lax–Friedrichs splitting, WENO-Z+ scheme, and third-order strong stability preserving Runge-Kutta time discretization. Our first problem is a simple one-dimensional transient problem with periodic boundary conditions, which is useful for constructing the core solver. Then, we move to the one-dimensional Rayleigh flow, which can handle flows with heat exchange and requires more detailed boundary treatment. The next problem is the quasi-one-dimensional nozzle flow with and without shock, where the boundary treatment needs a few adjustments. The first two-dimensional problem is the Ringleb flow, and despite being smooth, it has a curved wall as the left boundary. Finally, the last problem is a two-dimensional conical flow, which presents an oblique shock and an inclined straight line wall being the cone surface. We show that the designed accuracy is being reached for smooth problems, that high-resolution is being attained for non-smooth problems, and that our modifications produce similar results while providing a more generic way to treat solid walls.

解决CFD问题时，求解器或数字代码起着重要作用。根据现象和问题领域，设计这样的数字代码可能会很困难。一种策略是从简单的问题开始，然后将代码构建为构建块。这项工作的目的是提供有关计算解析和精确解的理论的详细综述，以及用于构造代码以解决具有高分辨率，任意域，非线性现象和可压缩流体的无粘性流体的最新数值方法。在矩形网格上。我们还建议对Lax-Wendroff逆过程进行实心墙处理，并对二维​​WENO型外推模板选择和权重进行修改，以处理更多一般情况。为了测试我们的修改，我们使用了有限差分方法Lax–Friedrichs分裂，WENO-Z +方案和三阶强稳定性，保留了Runge-Kutta时间离散。我们的第一个问题是带有周期边界条件的简单一维瞬态问题，对于构造核心求解器很有用。然后，我们转到一维瑞利流，该流可以通过热交换处理流，并且需要更详细的边界处理。下一个问题是有或没有冲击的准一维喷嘴流，其中边界处理需要一些调整。第一个二维问题是Ringleb流，尽管平滑，但它的左边界具有弯曲的壁。最后，最后一个问题是二维圆锥流，它呈现出倾斜冲击和倾斜的直线壁（圆锥表面）。