New Analytic Solution for Compressible Euler Equations with Bounded Far Field
Researchers have derived an exact analytic solution for imploding flows in the one-dimensional compressible Euler equations by replacing the unbounded far field condition in Kidder's formulation with a constant density cutoff. The study addresses a long-standing computational challenge: while smooth imploding solutions inspired by Guderley's work are theoretically well-understood, they are numerically unstable, whereas Kidder's solution is computable but unbounded. The findings are significant for computational fluid dynamics because they demonstrate that a non-centered rarefaction wave emerges from the cutoff and suppresses the implosion, providing a new exact solution that is both theoretically tractable and numerically stable.
This arXiv preprint presents an exact analytic solution to a modified version of the compressible Euler equations in one dimension. The authors build on Kidder's formulation of imploding solutions by introducing a constant density cutoff at the far field boundary, replacing the original unbounded condition. A key finding is that this modification causes a non-centered rarefaction wave to emerge from the cutoff region, which suppresses the implosion phenomenon. The authors support their theoretical predictions with numerical simulations across 8 figures. This work addresses a practical computational challenge in fluid dynamics: while classical imploding solutions have been well-studied theoretically, they present significant numerical difficulties, whereas this new approach offers both analytical tractability and computational stability.
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- arXiv physicsCenter
Self-similar imploding solutions of the 1D compressible Euler equations with a far field cutoff
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