Totally Analytical for All Re Pertinent CFD Vision 2030 Formulation

The totally analytical, truncation error annihilation (TEA) theory infused gaussian uniform measure δ spatially filtered NS PDE system weak formulation continuous Galerkin finite element (FE) p=1,2,3 completeness degree basis FaNS theory CFD that underlies the ∀Re pertinent, aerothermodynamics enabled Vision 2030 compliant Hypersonics CFD Laboratory is endowed with these optimal performance attributes: spatial discretization induced algebraic instability annihilated space-time discretization generated aliasing error annihilated - generates resolved scale monotone distributions 4th order accurate on any (!) mesh need for artificial/numerical stabilization annihilated need for physics-based closure modeling annihilated - FaNS theory validated to predict laminar-turbulent transition for Re>104 need for stabilized shock capture/ fitting annihilated - shock continuum monotone interpolation quantifies shock-boundary layer interaction modern approximation theory weak formulation mathematically rigorous predictions - error bounding by NS a priori given data - local, global error estimates in NS PDE intrinsic norms - uncertainty quantification of O(1) state variable mesh resolution adequacy via FaNS O(1;δ2;δ3) scaling - on-the-fly error quantization during regular solution adapted nonuniform mesh refinement - higher order asymptotic convergence via FE basis enrichment - theory compromise by non-smooth data quantified FaNS PDE nonlinear differentials precise translations to algebraic via calculus - cubic nonlinear translations generate FE hypermatrices - quadratic convergent Newton jacobian matrix differential calculus derived Detailed herein are validations pertinent to ∀Re FaNS theory prediction of aerothermodynamics, radiation and shock- boundary layer interaction impacted hypersonic shock layer submerged boundary layer laminar-turbulent transition influence on missile surface heating and pressure distributions.