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MAE Seminar Series: Hong Luo
April 5 @ 10:00 am - 11:00 am
Title:
On Enforcing Interface Conservation in Computational Fluid Dynamics
Abstract:
The necessity of enforcing conservation in computational elements or cells (element conservation) for discontinuous solutions is well understood and respected for solving conservation laws in computational fluid dynamics (CFD). In contrast, interface conservation, where the conservation across cell interfaces is enforced is long ignored, and yet is also ruled and required by the underlying physics just like element conservation. Violation of the interface conservation across discontinuities is the root cause why an exact discontinuous solution can never be achieved in shock capturing methods. The interface conservation is examined and explored in this presentation. An error indicator based on the interface conservation is then designed for h-adaptive grid methods to effectively detect and identify discontinuities, as the interface conservation can never be attained across the discontinuities. A moving discontinuous Galerkin (MDG) finite element method with interface conservation enforcement (MDG-ICE)1-2 is also developed for solving compressible flow problems with discontinuities based on the observation that the interface conservation can be satisfied, only when mesh interfaces are aligned with discontinuities. A number of numerical experiments are conducted to assess effectiveness of the interface-based error indicator and performance of the MDG-ICE method. Numerical results for a variety of discontinuous flow problems ranging from single phase, multi- phase, and hypersonic chemical and thermal non equilibrium reactive flows obtained indicate that the error indicator based on the interface conservation can effectively detect all types of discontinuities and under-resolved flow regions and the MDG-ICE method is able to reposition grid, align mesh interfaces with all types of discontinuities, and achieve the designed order of both h- and p-convergence even for discontinuous solutions.
Bio:
Dr. Luo is interested in computational fluid dynamics, computational magnetohydrodynamics, computational aeroacoustics, fluid-structure interaction, high-performance computing, and unstructured grid generation.
At the graduate level, Dr. Luo teaches Computation Fluid Dynamics (MAE 766). This course is concerned with the finite difference, finite volume, and finite element methods for solving the governing equations in fluid dynamics. Dr. Luo guides his students toward an expertise in numerical methods and strong capabilities in programming.
At the undergraduate level, he teaches Aerodynamics I (MAE 355) and Heat transfer fundamentals (MAE 310). In Aerodynamics I, he brings in examples over the wide range of flow speeds he has encountered in his own work, like low speed flow past an Indy-racing car, transonic flow around a Boeing 747, supersonic flow past a missile, and hypersonic flow past a space shuttle.
The students who work with Dr. Luo are drawn to his area of research because they find the numerical simulations and modeling, both technically interesting and intellectually challenging, and appreciate the increasingly important role that they play in science and engineering. These students appreciate its major impact on the development, design, and analysis of modern airplanes, high speed trains, advanced ships/submarines, high performance cars, new weapon systems, and nuclear reactors, leading to work opportunities in government/industry/national labs. Dr. Luo looks for students who are self-motivated, hard-working, and strong in mathematics and computer programming.
