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2d compressible four-state riemann problem simulation
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About the 2D Compressible Four-State Riemann Problem Simulation Project
This case presents a two-dimensional compressible Euler flow simulation of a four-state Riemann problem using NumericalAI (https://numericalai.net/). The domain is initialized with four different constant flow states separated by sharp discontinuities. Each region has distinct density, pressure, and velocity conditions, producing a complex interaction of shocks, contact discontinuities, expansion waves, and shear-driven structures. The simulation is performed on a uniform 499 × 499 grid using a high-order WENO reconstruction scheme and an approximate Riemann solver. As the solution evolves, the initially simple patch configuration develops into a rich multidimensional wave pattern. The high-pressure and high-density region drives strong compression waves into the surrounding lower-pressure states, while velocity differences across the interfaces generate curved contact surfaces and vortex-like roll-up features. The visualized fields include pressure, density, and x-velocity. The density field clearly captures the contact and shear structures, while the pressure field highlights the shock and compression regions. The velocity plot shows the development of localized acceleration and flow reversal near the central interaction zone. This benchmark is useful for evaluating shock-capturing performance, numerical dissipation, interface resolution, and the robustness of high-order compressible-flow solvers in multidimensional discontinuous flows.
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July 4th, 2026 Uploaded
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