Numerical Schemes for Scalar One-Dimensional Conservation Laws Lecture 12
Finite Volume Computational Cells Discretization t=T 7+1 c=△ t=m△t 011-1jj+-1J U SMA-HPC⊙2003MT Hyperbolic Equations 1
Finite Volume Cell averages Discretization We think of in as representing cell averages 1 a(a, t") da C SMA-HPC⊙2003MT Hyperbolic Equations 2
Conservative Definition Methods Applying integral form of conservation law to a cell 3 d dt ad=-f((+,1)-f(a(a=,D) suggests in+l △t△a= T+1= △t C j+号 F SMA-HPC⊙2003MT Hyperbolic Equations 3
Conservative Numerical Flux function Methods +=F(a1b,①31+1,…,,…,句+) and F is a numerical flux function of l+r+1 arguments that satisfies the following consistency condition F(u, a 儿。L )=f(u) 7+1 SMA-HPC⊙2003MT Hyperbolic Equations 4