Abstract:

Even when initial conditions are smooth, the solutions of non linear hyperbolic PDEs develop discontinuities as they evolve in time. When computing numerical solutions for these type of problems, one must employ methods that are capable of detecting discontinuities and to resolve them accurately. Numerical methods based on central differencing are not only efficient for this purpose, but also simple to implement. Although the efficiency and robustness of central schemes for solving Euler's equations of gas dynamics and other relatively small systems of conservation laws have been demonstrated, little is known about their performance for solving more complex systems such as the equations of Ideal Magnetohydrodynamics (MHD). This talk will present recent results that show how central schemes offer a resolution and an accuracy for solving MHD equations in one and two space dimensions comparable to those of less efficient existing methods.