{"uid":"cap_GF95gc0hPVqMhMJvQcxb9","slug":"ideal-gas-euler-riemann-complete-shock-rarefaction-contact-state-solver-06446e6f","name":"Ideal Gas Euler-Riemann Complete Shock-Rarefaction-Contact State Solver","description":"Recover all waves and sampled conservative states of an explicit compressible gas discontinuity.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B010/ideal-gas-euler-riemann-complete-shock-rarefaction-contact-state?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["eulerRiemann"],"properties":{"eulerRiemann":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["left","right","gamma","similarity_coordinates"],"properties":{"left":{"type":"object","required":["density","velocity","pressure"],"properties":{"density":{"type":"number","maximum":10000,"minimum":0.000001},"pressure":{"type":"number","maximum":1000000,"minimum":0.000001},"velocity":{"type":"number","maximum":10000,"minimum":-10000}},"additionalProperties":false},"gamma":{"type":"number","maximum":2,"minimum":1.01},"right":{"type":"object","required":["density","velocity","pressure"],"properties":{"density":{"type":"number","maximum":10000,"minimum":0.000001},"pressure":{"type":"number","maximum":1000000,"minimum":0.000001},"velocity":{"type":"number","maximum":10000,"minimum":-10000}},"additionalProperties":false},"similarity_coordinates":{"type":"array","items":{"type":"number","maximum":100000,"minimum":-100000},"maxItems":32,"minItems":1}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_6qtfUUpsbXnLX3CnZH_eO","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Solves the complete Euler-Riemann problem for a compressible ideal gas discontinuity, recovering all wave structures (shocks, rarefactions, contact discontinuities) and sampled conservative states at specified similarity coordinates.","exampleAgentPrompt":"Solve the exact Euler-Riemann problem for an ideal gas with gamma=1.4, left state density=1.0 velocity=0.0 pressure=1.0, right state density=0.125 velocity=0.0 pressure=0.1 (classic Sod tube), and sample the complete conservative state solution at similarity coordinates -2.0, -0.5, 0.0, 0.5, 1.75, and 3.0.","exampleUseCases":[{"title":"Sod shock tube benchmark verification","prompt":"Run the classic Sod shock tube Riemann problem with gamma=1.4, left state density=1.0 velocity=0.0 pressure=1.0 and right state density=0.125 velocity=0.0 pressure=0.1, and give me the full wave structure plus sampled states at x/t coordinates -1.0, 0.0, 0.5, 1.0, and 2.0."},{"title":"Hypersonic shock interaction analysis","prompt":"I need to solve a Riemann problem for a strong shock: gamma=1.4, left state density=5.0 velocity=800.0 pressure=50000.0, right state density=1.2 velocity=0.0 pressure=101325.0 — sample the resulting states at similarity coordinates -100, 0, 200, 500, and 1000 so I can see the shock and contact positions."},{"title":"Numerical flux validation for CFD solver","prompt":"Compute the exact Riemann solution for a gas with gamma=1.667 (monatomic ideal gas), left state density=2.0 velocity=-1.0 pressure=0.4, right state density=1.0 velocity=1.0 pressure=0.4, and sample it at coordinates -3.0, -1.0, 0.0, 1.0, and 3.0 so I can validate my numerical flux against the exact answer."}],"resultDescription":"Returns all wave speeds and types (shock, rarefaction head/tail, contact discontinuity), the intermediate star-region pressure and velocity, and the full conservative state (density, momentum, energy) sampled at each requested similarity coordinate (x/t value) across the Riemann fan.","failureModes":["Left or right state density or pressure outside allowed range (0.000001–10000 / 0.000001–1000000) → validation error","Gamma outside range [1.01, 2.0] → rejected input","More than 32 similarity coordinates provided → schema violation","Vacuum formation (opposing rarefactions that deplete pressure to zero) → may return error or degenerate state","Similarity coordinates outside [-100000, 100000] → rejected","Missing required left/right state fields → 400-level error"],"whenToPreferThis":"Use this endpoint when you need the mathematically exact solution to the 1D Euler Riemann problem for an ideal gas — not an approximate or linearized Riemann solver. Ideal for validating CFD codes, generating reference solutions for shock tube problems, computing numerical fluxes exactly, or studying wave interaction structure. Prefer this over approximate Riemann solvers (Roe, HLLC, etc.) when exact wave speeds and intermediate states are needed. Only supports ideal (calorically perfect) gas with constant gamma; not suitable for real-gas equations of state.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:40:45.025Z","isFirstParty":false,"canonicalSlug":"ideal-gas-euler-riemann-complete-shock-rarefaction-contact-state-solver-06446e6f"}