Finite volume schemes often have difficulties to resolve the low Mach number (incompressible) limit of the Euler equations. Incompressibility is only non-trivial in multiple spatial dimensions. Low Mach fixes, however generally are applied to the one-dimensional method and the method is then used in a dimensionally split way. This often reduces its stability. Here, it is suggested to keep the one-dimensional method as it is, and only to extend it to multiple dimensions in a particular, all-speed way. This strategy is found to lead to much more stable numerical methods. Apart from the conceptually pleasing property of modifying the scheme only when it becomes necessary, the multi-dimensional all-speed extension also does not include any free parameters or arbitrary functions, which generally are difficult to choose, or might be problem dependent. The strategy is exemplified on a Lagrange Projection method and on a relaxation solver.

中文翻译：

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笛卡尔网格上欧拉方程的真正多维全速方案

有限体积方案通常难以解决欧拉方程的低马赫数（不可压缩）极限。不可压缩性在多个空间维度上都是不平凡的。但是，低马赫数修补程序通常应用于一维方法，然后以维拆分的方式使用该方法。这通常会降低其稳定性。在这里，建议保持一维方法不变，仅以特定的全速方式将其扩展到多个维度。发现该策略导致更稳定的数值方法。除了仅在必要时才修改方案的概念上令人愉悦的特性外，多维全速扩展还不包括任何自由参数或任意函数，这些自由参数或任意函数通常难以选择，或者可能与问题相关。