CoDeS supplies a compression-aligned tensor stress from a modified-Helmholtz solve that activates only at shocks and remains inactive in expansions, contacts, and shear.
arXiv preprint arXiv:2411.15121 (2024)
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abstract
Partial differential equations describing compressible fluids are prone to the formation of shock singularities, arising from faster upstream fluid particles catching up to slower, downstream ones. In geometric terms, this causes the deformation map to leave the manifold of diffeomorphisms. Information geometric regularization addresses this issue by changing the manifold geometry to make it geodesically complete. Empirical evidence suggests that this results in smooth solutions without adding artificial viscosity. This work makes a first step towards understanding this phenomenon rigorously, in the setting of the unidimensional pressureless Euler equations. It shows that their information geometric regularization has smooth global solutions. By establishing $\Gamma$-convergence of its variational description, it proves convergence of these solutions to entropy solutions of the nominal problem, in the limit of vanishing regularization parameter. A consequence of these results is that manifolds of unidimensional diffeomorphisms with information geometric regularization are geodesically complete.
years
2026 3representative citing papers
A thermodynamic extension of information geometric regularization for compressible flows introduces an anisotropic stress tensor and an elliptic equation that mitigates cusp singularities in simulations while preserving inviscid benefits.
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A Compression-Directional Entropic Stress Method for Shock-Regularized Compressible Flow
CoDeS supplies a compression-aligned tensor stress from a modified-Helmholtz solve that activates only at shocks and remains inactive in expansions, contacts, and shear.
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Thermodynamically Constrained Information Geometric Regularization for Compressible Flows
A thermodynamic extension of information geometric regularization for compressible flows introduces an anisotropic stress tensor and an elliptic equation that mitigates cusp singularities in simulations while preserving inviscid benefits.
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