Tianshi Lu PhD, Dr.

Overview

Tianshi Lu is an Associate Professor of Mathematics. After obtaining his Ph.D. in Applied Mathematics at SUNY at Stony Brook in 2005, he worked as a Research Associate and an Assistant Computational Scientist on computational fluid dynamics at Brookhaven National Laboratory. He joined Wichita State University in 2008 with promotion to Associate Professor in 2012.

Tianshi Lu’s research ranges from numerical analysis to computational physics and statistics. He specializes in multiphase computational fluid dynamics and magnetohydrodynamics simulations, free surface flows, numerical schemes for advection-dominated systems, as well as computational quantum optics, spectral functions and Zeta functions on manifolds, and random fields on randoms. His current research involves modeling and simulation of multiphase flows in additive manufacturing, superconvergence of discontinuous Galerkin methods for hyperbolic conservation laws, and vector random fields on homogeneous spaces.

Academic Interests and Expertise

• Multiphase Flows
• Numerical Analysis
• Random Fields

Areas of Teaching Interest

• Numerical Linear Algebra
• Numerical Analysis of PDE

Publications

• Lu, N. Leonenko, C. Ma. Series representations of isotropic vector random fields on balls. Stat. Probabil. Lett. 156, 108583 (2020).
• Lu, C. Ma. Isotropic covariance matrix functions on compact two-point homogeneous spaces. J. Theor. Probab. (2019). https://doi.org/10.1007/s10959-019-00920-1 
• Lu, T. Jeffres, K. Kirsten. Zeta function of self-adjoint operators on surfaces of revolution. J. Phys. A: Math. Theor. 48, 145204 (2015).
• Lu. Wave propagation in bubbly fluids and cavitation mitigation. Wave Propagation, Ed. Gomes Mateus, Academy Publish, 309-332 (2014).
• Kostogorova-Beller, T. Lu. Numerical Modeling of Experimentally Obtained Lightning Arc Root Damage in Metal Sheets. Int’l J. Eng. Prac. Res. 2, 139-147 (2013).
• Jeffres, K. Kirsten, T. Lu. Zeta function on surfaces of revolution. J. Phys. A: Math. Theor. 45, 345201 (2012).
• Lu. Population Inversion by Chirped Pulses. Phys. Rev. A 84, 033411 (2011).
• B. Parks, T. Lu, R. Samulyak. Charging and EB Rotation of Ablation Clouds Surrounding Refueling Pellets in Hot Fusion Plasmas. Physics of Plasmas 16, 060705 (2009).
• Lu, J. Du, R. Samulyak. A Numerical Algorithm for Magnetohydrodynamics of Ablated Materials. J. Nanosci. Nanotechnol. 8, 3674-3685 (2008).
• Lu, Z. L. Xu, J. Glimm, R. Samulyak, X. M. Ji. Dynamic Phase Boundaries for Compressible Fluids. SIAM J. Sci. Comput. 30, 895-915 (2008).
• Samulyak, T. Lu, P. Parks, J. Glimm, X. Li. Simulation of Pellet Ablation for Tokamak Fueling with ITAPS Front Tracking. Journal of Physics: Conf. Series 125, 012081 (2008).
• Lu, X. Miao, H. Metcalf. Nonadiabatic Transitions in Finite-Time Adiabatic Rapid Passage. Phys. Rev. A 75, 063422 (2007).
• Lu, R. Samulyak, J. Glimm. Direct Numerical Simulations of Bubbly Flows and Application to Cavitation Mitigation. J. Fluids Eng. 129, 595-604 (2007).
• Samulyak, T. Lu, P. B. Parks. A Magnetohydrodynamics Simulation of Pellet Ablation in the Electrostatic Approximation. Nucl. Fusion 47, 103-118 (2007).
• Glimm, B. Fix, X.L. Li, J. Liu, X. Liu, T. Lu, R. Samulyak, Z. Xu. Front Tracking under TSTT. Astronomical Society of the Pacific 359, 15-24 (2006).
• Xu, M. Kim, T. Lu, W. Oh, J. Glimm, R. Samulyak, X. Li, C. Tzanos. Discrete Bubble Modeling of Unsteady Cavitating Flow. Int. J. Multiscale Comp. Eng. 4, 601-616 (2006).
• Samulyak, Y. Prykarpatskyy, T. Lu, J. Glimm, Z. Xu, M.N. Kim. Comparison of Heterogeneous and Homogenized Numerical Models of Cavitation. Int. J. Multiscale Comp. Eng. 4, 377-390 (2006).
• Lu, X. Miao, H. Metcalf. The Bloch Theorem on the Bloch Sphere. Phys. Rev. A 71, 061405 (2005).
• Jin, X.F. Liu, T. Lu, B. Cheng, J. Glimm, D.H. Sharp. Rayleigh-Taylor Mixing Rates for Compressible Flow. Phys. Fluids 17, 024104 (2005).
• Samulyak, T. Lu, Y. Prykarpatskyy. Direct and Homogeneous Numerical Approaches to Multiphase Flows and Applications. Lecture Notes in Computer Science 3039, 653-660 (2004), Springer-Verlag Berlin Heidelberg.
• Lu, C. Ma, F. Wang. Series expansions of fractional Brownian motions and strong local nondeterminism of bifractional Brownian motions on balls and spheres. Submitted to Theory of Probability and Its Applications.
• Lu, J. Du, C. Ma. Stochastic comparison for elliptically contoured random fields. Submitted to Journal of Applied Probability.
• Rahmati, T. Lu. Superconvergence of discontinuous Galerkin method for scalar and vector linear advection equations. Submitted to J. Sci. Comput.