View Proposal #219
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| ID | 219 |
|---|---|
| First Name | Haseena |
| Last Name | Ahmed |
| Institution | Iowa State University |
| Speaker Category | graduate student |
| Title of Talk | Alternating evolution (AE) schemes for hyperbolic conservation laws |
| Abstract | An alternating evolution (AE) system is proposed which is an accurate approximation to systems of hyperbolic conservation laws. We develop a class of local Alternating Evolution (AE) schemes, where we take advantage of high accuracy of the proposed AE approximation. Our approach is based on a sliding average of the AE system over an interval of [x − \Delta x, x + \Delta x]. The numerical scheme is then constructed by sampling the averaged system over alternating grids. Higher order accuracy is achieved by a combination of high-order polynomial reconstruction from the obtained averages and a stable Runge-Kutta discretization in time. The AE schemes have the advantage of easier formulation and implementation, and efficient computation of the solution. For the first and second order local AE schemes applied to scalar laws, we prove the numerical stability in the sense of satisfying the maximum principle and total variation diminishing (TVD) property. Numerical tests for both scalar conservation laws and compressible Euler equations are presented to demonstrate the high order accuracy and capacity of these AE schemes. |
| Subject area(s) | Applied Mathematics, Numerical Analysis |
| Suitable for undergraduates? | Yes |
| Day Preference | |
| Computer Needed? | N |
| Bringing a laptop? | Y |
| Overhead Needed? | Y |
| Software requests | Adobe Acrobat reader |
| Special Needs | |
| Date Submitted | 2/20/2008 |
| Year | 2008 |