An entropy-variables-based formulation of residual distribution schemes for non-equilibrium flows

An enthalpy‐preserving shock‐capturing term for residual distribution schemes

“…The B x scheme and several of its variants have been used to compute hypersonic flow fields with crisp shock capture and good convergence toward steady‐state properties. However, as we shall discuss in Section 4, the dissipation that the B x scheme provides across a strong bow shock wave is uneven and may lead to perturbations in the postshock region that eventually spoil the calculation . In upcoming sections, we will consider strategies to devise better‐behaved RD shock‐capturing terms.…”

“…However, as we shall discuss in Section 4, the dissipation that the Bx scheme provides across a strong bow shock wave is uneven and may lead to perturbations in the postshock region that eventually spoil the calculation. 32,43 In upcoming sections, we will consider strategies to devise better-behaved RD shock-capturing terms. In order to accomplish this goal, we need to delve first on the relation between RD schemes and stabilized FE methods.…”

“…One difference between the stabilized FE method of Kirk and our RD schemes lies in the definition of the shock detector, where μ art in Equation has a residual character and the shock detector θ in Equation has not. The modification to provide θ with a residual character is straightforward; however, extensive experience with the detector of Dobeš shows that shock waves are captured crisply across few elements and fair convergence to steady state is obtained (see other works).…”

“…Residual distribution methods were employed successfully for the discretization and solution of advection-diffusion scalar equations [21][22][23][24] and for the compressible Navier-Stokes equations in the context of transonic aerodynamics 19,[25][26][27] in other works. In the hypersonic field, the method has been applied to double-cone configurations 28,29 and blunt-body problems, both in shock-capturing [30][31][32] and shock-fitting [33][34][35][36] contexts.…”

On the well-posedness of the multi-dimensional Roe–Liu–Vinokur linearization for residual distribution schemes

“…In attention to the limited space in Short Notes, the governing equations and their discretized version are presented very briefly in section 2. The reader interested will find the complete details on the application of the Residual Distribution (RD) method to the n s species, two-temperature TCNEQ model in reference [7]. Next, the multi-dimensional linearization procedure is described in section 3; an application case of the multi-dimensional linearization is also presented, and several of its shortcomings are identified.…”