Numerical Study of Space Time Conservation Element And Solution Element Method for Conservation Laws
|關鍵字:||保守律;conservation laws;discontinuous flux;conservation element and solution element|
In this thesis, the main task is to solve conservation laws with a discontinuous flux function in space applying the space time conservation elements and solution elements method (CESE). CESE is an explicit method with accuracy of second order at least. We will review the key idea of CESE by considering an simple linear case. Next, CESE method for conservation laws with non-linear flux will be derived and applied to discontinuous flux function. On the interface, the basic strategy is to apply the Newton's method. Also, the Steffensen's method is applied for avoiding taking complicated derivatives. Our new modified CESE method is accurate of order 2 at least in $L_1$ and $L_2$ norms. Then, we perform the modified CESE method for the cases of discontinuous flux function, $f$ and $g$, which satisfy the assumption that either $f$ is convex and $g$ is concave or $f$ is concave and $g$ is convex. Several numerical examples with Riemann problems are also performed and presented.
|Appears in Collections:||Thesis|