Abstract
A fully multidimensional flux formulation for solving nonlinear conservation laws of hyperbolic type is introduced to perform calculations on unstructured grids made of triangular or quadrangular cells. Fluxes are computed across dual median cells with a multidimensional 2D Riemann Solver (R2D Solver) whose intermediate states depend on either a three (on triangle R2DT solver) of four (on quadrangle, R2DQ solver) state solutions prescribed on the three or four sides of a gravity cell. Approximate Riemann solutions are computed via a linearization process of Roe`s type involving multidimensional effects. Moreover, a monotonous scheme using stencil and central Lax-Friedrichs corrections on sonic curves are built in. Finally, high order accurate ENO-like (Essentially Non Oscillatory) reconstructions using plane and higher degree polynomial limitations are defined in the set up of finite element Lagrange spaces P{sub k} and Q{sub k} for k{>=}0, on triangles and quadrangles, respectively. Numerical experiments involving both linear and nonlinear conservation laws to be solved on unstructured grids indicate the ability of our techniques when dealing with strong multidimensional effects. An application to Euler`s equations for the Mach three step problem illustrates the robustness and usefulness of our techniques using triangular and quadrangular grids. (Author). 33 refs., 13 figs.
Citation Formats
Lafon, F.
On fully multidimensional and high order non oscillatory finite volume methods, I.
France: N. p.,
1992.
Web.
Lafon, F.
On fully multidimensional and high order non oscillatory finite volume methods, I.
France.
Lafon, F.
1992.
"On fully multidimensional and high order non oscillatory finite volume methods, I."
France.
@misc{etde_10129587,
title = {On fully multidimensional and high order non oscillatory finite volume methods, I}
author = {Lafon, F}
abstractNote = {A fully multidimensional flux formulation for solving nonlinear conservation laws of hyperbolic type is introduced to perform calculations on unstructured grids made of triangular or quadrangular cells. Fluxes are computed across dual median cells with a multidimensional 2D Riemann Solver (R2D Solver) whose intermediate states depend on either a three (on triangle R2DT solver) of four (on quadrangle, R2DQ solver) state solutions prescribed on the three or four sides of a gravity cell. Approximate Riemann solutions are computed via a linearization process of Roe`s type involving multidimensional effects. Moreover, a monotonous scheme using stencil and central Lax-Friedrichs corrections on sonic curves are built in. Finally, high order accurate ENO-like (Essentially Non Oscillatory) reconstructions using plane and higher degree polynomial limitations are defined in the set up of finite element Lagrange spaces P{sub k} and Q{sub k} for k{>=}0, on triangles and quadrangles, respectively. Numerical experiments involving both linear and nonlinear conservation laws to be solved on unstructured grids indicate the ability of our techniques when dealing with strong multidimensional effects. An application to Euler`s equations for the Mach three step problem illustrates the robustness and usefulness of our techniques using triangular and quadrangular grids. (Author). 33 refs., 13 figs.}
place = {France}
year = {1992}
month = {Nov}
}
title = {On fully multidimensional and high order non oscillatory finite volume methods, I}
author = {Lafon, F}
abstractNote = {A fully multidimensional flux formulation for solving nonlinear conservation laws of hyperbolic type is introduced to perform calculations on unstructured grids made of triangular or quadrangular cells. Fluxes are computed across dual median cells with a multidimensional 2D Riemann Solver (R2D Solver) whose intermediate states depend on either a three (on triangle R2DT solver) of four (on quadrangle, R2DQ solver) state solutions prescribed on the three or four sides of a gravity cell. Approximate Riemann solutions are computed via a linearization process of Roe`s type involving multidimensional effects. Moreover, a monotonous scheme using stencil and central Lax-Friedrichs corrections on sonic curves are built in. Finally, high order accurate ENO-like (Essentially Non Oscillatory) reconstructions using plane and higher degree polynomial limitations are defined in the set up of finite element Lagrange spaces P{sub k} and Q{sub k} for k{>=}0, on triangles and quadrangles, respectively. Numerical experiments involving both linear and nonlinear conservation laws to be solved on unstructured grids indicate the ability of our techniques when dealing with strong multidimensional effects. An application to Euler`s equations for the Mach three step problem illustrates the robustness and usefulness of our techniques using triangular and quadrangular grids. (Author). 33 refs., 13 figs.}
place = {France}
year = {1992}
month = {Nov}
}