PPPS-2013: High-order numerical methods for KEEN wave Vlasov-Poisson simulations

Summary form only given. KEEN waves¹ provided a challenging test case for Vlasov-Poisson numerical solvers since they involve highly nonstationary, multiple-harmonic self-organized kinetic states. They require high resolution in the phase space region around the phase velocity of the drive wave. The standard splitting method with cubic spline interpolation has proven very robust and still provides an excellent reference method. We investigate here how it compares to arbitrary high order spline and Lagrange interpolation. The high order interpolation methods have been coded very simply using a periodic interpolation in both directions and using FFT. The code has also been ported very successfully to GPU². The region of interest being localized in velocity space, around the phase velocity of the KEEN wave, we have also developed a mapped grid method enabling very high resolution in that region without penalty outside. We shall investigate the benefits and drawbacks of using a non uniform mesh for KEEN Wave simulations as we look towards KEEN-KEEN interactions in multiple dimensions.