Shock waves in high-speed fluid dynamics produce near-discontinuities in the fluid momentum, density, and energy. Most contemporary works use artificial viscosity or limiters as numerical mitigation of the Gibbs--Runge oscillations that result from traditional numerics. These approaches face a delicate balance in achieving sufficiently regular solutions without dissipating fine-scale features, such as turbulence or acoustics. Recent work by Cao and Schäfer introduces information geometric regularization (IGR), the first inviscid regularization method for fluid dynamics. IGR replaces shock singularities with smooth profiles of adjustable width, without dissipating fine-scale features. This work provides a strategy for the practical use of IGR in finite-volume-based numerical methods. We illustrate its performance on canonical test problems and compare it against established approaches based on limiters and Riemann solvers. Results show that the finite volume IGR approach recovers the expected solutions in all cases. Across canonical benchmarks, IGR achieves accuracy competitive with WENO and LAD shock-capturing schemes in both smooth and discontinuous flow regimes. The IGR approach is computationally light, with meaningfully fewer memory accesses and arithmetic operations per time step.

翻译：高速流体动力学中的激波会在流体动量、密度和能量中产生近乎间断的现象。当前大多数研究采用人工粘性或限制器作为数值手段，以抑制传统数值方法产生的Gibbs-Runge振荡。这些方法需要在获得足够光滑的解与不耗散精细尺度特征（如湍流或声学现象）之间取得微妙平衡。Cao和Schäfer近期提出的信息几何正则化（IGR）是首个针对流体动力学的无粘性正则化方法。IGR在不耗散精细尺度特征的前提下，将激波奇异性替换为宽度可调的光滑轮廓。本研究为基于有限体积的数值方法中IGR的实际应用提供了策略。我们通过经典测试问题展示了其性能，并与基于限制器和Riemann求解器的成熟方法进行了对比。结果表明，有限体积IGR方法在所有案例中均能恢复预期解。在经典基准测试中，IGR在光滑和间断流场区域均达到了与WENO和LAD激波捕捉方案相媲美的精度。IGR方法计算量轻便，每个时间步的内存访问次数和算术运算量显著减少。