Numerical Methods and Stability

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Structural Limits of Linear Eddy-Viscosity Models in the Planar Jet

The jet spreads correctly. The decay law matches DNS. The residuals drop six orders. Mass imbalance falls below . And yet the turbulence state at the centerline is mathematically impossible under the closure I’m using. This isn’t a calibration problem. It’s not a grid issue. It’s not even a turbulence model problem in the way […]

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When pressure-based solvers silently break conservation

Okay, real talk for a minute. Last month, I almost submitted a paper with results that were mathematically beautiful and physically impossible. My pressure-based solver said everything was perfect—residuals at , drag coefficient stable to four decimals. Then my advisor asked the simple question: “How much mass is actually entering versus leaving the domain?” Turns out,

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Time-Step Independence Is Not What You Think It Is: The Stiffness vs. CFL Trap

I was simulating vortex shedding behind a cylinder at Re = 100. My explicit compressible solver gave plausible results at Δt = 1e-5 seconds, but to be “safe,” I ran it at Δt = 1e-7. The simulation took four days to capture three shedding cycles. When I mentioned this to a postdoc, she asked: “Why

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