Solution of Adjoint Equations

Solution of Adjoint Equations Truly unstructured grids with shocks and thin reaction zones result in very poorly conditionedadjoint systems Further complicated by true discrete adjoint of second order discretization with non-linear limiters Careful choice of linear system solvers is required and from the viewpoint of efficiency and robustness, this choice is problem-dependent For the full system, local LU decomposition is used with GMRES iterations 2D Laminar SBLI @ Rex = 3x105 Cond number O (1x107) Full system with combustion Cond number O(1x1014)

Solution of Adjoint Equations

Solution of Adjoint Equations

Presentation Transcript

Solution of Simultaneous Linear Equations (AX=B)

Solution of linear equations using Gaussian elimination

Numerical solution of Differential and Integral Equations

Solution of Systems of Linear Equations

Solution of Linear State- Space Equations

Numerical Solution of Differential Equations

Adjoint TM5

Solution of Differential Equations

Numerical Solution of Coupled Differential Equations

Solution of linear equations using Gaussian elimination

Solution of the St Venant Equations / Shallow-Water equations of open channel flow

Solution of the St Venant Equations / Shallow-Water equations of open channel flow

Solution of Equations by Iteration

Solution of Nonlinear Equations Topic: Bisection method

Solution of Simultaneous Linear Equations (AX=B)

Solution of Hartree-Fock equations

adjoint matrix

Solution of Nonlinear Equations Topic: Bisection method