Strongly Coupled Computation of Material Response and Nonequilibrium Flow for Hypersonic Ablation

A = Jacobian matrix a = speed of sound, m∕s C = source term vector E = total energy, J∕kg e = internal energy vector, J∕kg F = inviscid flux tensor Fd = diffusive flux tensor Fo = Forchheimer number G = flux tensor, F − Fd − uU h = enthalpy, J∕kg h = species enthalpy vector, J∕kg hr = recovery enthalpy, J∕kg I = identity matrix J = directional species diffusion flux tensor, kg∕m K = permeability, m L = eigenvector similarity transformation matrix l = euclidian norm l = characteristic length, m _ m 0 0 0 = volumetric mass source term, kg∕m ⋅ s _ m 0 0 = mass rate, kg∕m ⋅ s p = pressure, Pa pη = total pressure, Pa q = surface heat transfer rate, W∕m _ q 0 0 = internal heat flux, W∕m R = right-hand side term r = distance vector, m S, S = surface, m T = temperature, K t = time, s U = conservative vector u, u, v = velocity, m∕s w = node velocity, m∕s _ wv = vibrational energy relaxation source term, J∕m ⋅ s _ w = source term, kg∕m ⋅ s, J∕m ⋅ s V = volume, m x, y = coordinates, m Y = species mass fraction, kg∕kg β = Forchheimer coefficient, m−1 Δ = increment Λ = eigenvalue matrix μ = dynamic viscosity, Pa ⋅ sPa-s ρ = total density, kg∕m τ = viscous tensor, Pa φ = porosity, m∕m ψ = damping factor