Assessment of implicit operators for the upwind point Gauss–Seidel method on unstructured meshes

Implicit LU-SGS algorithm for high-order methods on unstructured grid with p-multigrid strategy for solving the steady Navier–Stokes equations

“…Besides, for a specific direction of the harmonic wave solution ðh ¼ 0Þ of the 2D linear convection equation, the implicit iterative scheme shows an amplification factor which is close to 1 for a wave number range equal to half of the period of Eq. (26). For wave numbers higher than half of the period the amplification factor is close to zero.…”

“…In [25,26] this analysis was applied to implicit schemes on Cartesian grids for classical upwind and central scheme. We present the analysis on triangular grids, defined by a generating pattern, and for a general SV schemes.…”

“…The damping properties of the implicit method are evaluated with a Von Neumann stability analysis for a model 2D linear advection equation. In [25,26] this analysis was applied to implicit schemes on Cartesian grids for classical upwind and central schemes. In the present work the analysis is on triangular grids defined by a generating pattern, and for high-order SV schemes.…”

“…However, Eq (26). has N CV eigenvalues for each K and, as was pointed out Spatial shape of the eigenvectors of the direct + BE method applied to 2D linear convection equation.…”

Implicit multigrid schemes for challenging aerodynamic simulations on block-structured grids

“…With this choice, the block-diagonal entries of the Jacobian reduce to diagonal matrices, enabling the construction of implicit schemes particularly robust and free of matrix inversions. However, it was shown that this choice does degrade the achievable rate of convergence [46,7,15], and using characteristic-splitting of the flux Jacobians is preferable. Acknowledging this fact, we favor the matrix dissipation scheme in the definition of the residual, whose first-order equivalent is the upwind flux of Roe [33].…”