• Designed and implemented a new high order numerical solver for partial differential equations with non-continuous initial conditions based on WENO scheme.

• Developed a program to explore the relations between perturbations in initial conditions and growth rate of instabilities in solutions of partial differential equations related to fluid dynamics.

• Worked out a new conservative front tracking algorithm to simulate instabilities in fluid mixings.

• Conducted several large-scale numerical simulations in complex fluid dynamics.

• Developed multi-step scenario predictions based on a statistic model on a trading platform and enhanced its performance by parallel computing.

• Designed a program to read and process stock market data from a real-time database, detect structure breaks of the market and send warning messages automatically to users when a structure break is detected.