Engineering topics
Yu, Kwangmin
Publications and source records attributed to Yu, Kwangmin.
AP-Cloud: Adaptive Particle-in-Cloud method for optimal solutions to Vlasov–Poisson equation
We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov–Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes of computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques.
Second order upwind Lagrangian particle method for Euler equations
A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and long term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.
Experience with OpenMP for MADX-SC
MADX-SC allows the treatment of frozen space charge using beam-beam elements in a thin lattice, i.e. one can take advantage of the standard set-up of MAD-X lattices without the need for specialized codes for the space-charge (SC) evaluation. The idea is to simulate over many turns without the problem of noise as in the PIC SC codes. For the examples under study, like the PS and RHIC, it would be desirable to simulate up to 1 million turns or more. To this end one had to make an effort to optimize the scalar speed and, most importantly, get a speed-up of approximately a factor of 5 using OpenMP.