Accuracy-preserving boundary flux quadrature for finite-volume discretization on unstructured grids

Improved second-order hyperbolic residual-distribution scheme and its extension to third-order on arbitrary triangular grids

“…The third-order edge-based finite-volume scheme has similar properties: it is third-order accurate with the linear elements and requires highorder normals for the Neumann boundary condition as demonstrated in Ref. [26]. We also explain in details the quadratic reconstruction of the boundary normals on the solid surfaces that are represented with the linear elements; the details are given in Appendix A.…”

“…The finite-volume (FV) scheme of Ref. [26] is another example, where a third-order solution was obtained on the linear elements with a quadratic reconstruction of the boundary normals for curved boundaries. The third-order residual-distribution schemes of Refs.…”

“…Our proposed thirdorder scheme is among these schemes, and is more aligned with the FV scheme of Ref. [26] because the proposed third-order scheme here produces third-order solution gradients for geometries containing curved boundaries that are represented by straight-sided meshes.…”

EBR-WENO scheme for solving gas dynamics problems with discontinuities on unstructured meshes

“…Потоки через грани контрольного объёма узла i, помеченные условием непротекания, вычисляются по формуле h = (0, p i n, 0) T , где p i -давление в соответствую-щем узле [24]. Более точный алгоритм, обеспечивающий точность на линей-ной функции, предполагает осреднение с учётом соседних ячеек (см., напри-мер, [34]), однако улучшения качества счёта при его использовании нами на практике замечено не было.…”

A first-order hyperbolic system approach for dispersion

“…The schemes proposed with the hyperbolic formulation of PDE systems are upwind and highly accurate for both the solution u and its gradient u x , and have a natural potential for extension on arbitrary unstructured meshes as illustrated in Refs. [22,23]. The presence of a third-order derivative term in form (c), however, introduces discretization difficulties, which are often related to the understanding of the type of stencil that is required to approximate these high-order derivative terms, the stability of the method used, and the imposition of boundary conditions.…”