37 citations · 133 across the 14 of their papers we have counts for
9 papers · 1 filter
RelaxNet: A structure-preserving neural network to approximate the Boltzmann collision operator
Tianbai Xiao, Martin Frank
This paper addresses a neural network-based surrogate model that provides a structure-preserving approximation for the fivefold collision integral. The notion originates from the s…
A flux reconstruction stochastic Galerkin scheme for hyperbolic conservation laws
Tianbai Xiao, Jonas Kusch, Julian Koellermeier +1
The study of uncertainty propagation poses a great challenge to design numerical solvers with high fidelity. Based on the stochastic Galerkin formulation, this paper addresses the…
A flux reconstruction kinetic scheme for the Boltzmann equation
Tianbai Xiao
It is challenging to solve the Boltzmann equation accurately due to the extremely high dimensionality and nonlinearity. This paper addresses the idea and implementation of the firs…
Using neural networks to accelerate the solution of the Boltzmann equation
Tianbai Xiao, Martin Frank
One of the biggest challenges for simulating the Boltzmann equation is the evaluation of fivefold collision integral. Given the recent successes of deep learning and the availabili…
Modeling and Simulation of Non-equilibrium Flows with Uncertainty Quantification
Tianbai Xiao
In the study of gas dynamics, theoretical modeling and numerical simulation are mostly set up with deterministic settings. Given the coarse-grained modeling in theories of fluids,…
A stochastic kinetic scheme for multi-scale plasma transport with uncertainty quantification
Tianbai Xiao, Martin Frank
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochasti…
A stochastic kinetic scheme for multi-scale flow transport with uncertainty quantification
Tianbai Xiao, Martin Frank
Gaseous flows show a diverse set of behaviors on different characteristic scales. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist betw…
A velocity-space adaptive unified gas kinetic scheme for continuum and rarefied flows
Tianbai Xiao, Kun Xu, Qingdong Cai
In this paper, a unified gas kinetic scheme with adaptive velocity space (AUGKS) for multiscale flow transport will be developed. In near-equilibrium flow regions, particle distrib…
A Well-Balanced Unified Gas-Kinetic Scheme for Multiscale Flow Transport Under Gravitational Field
Tianbai Xiao, Qingdong Cai, Kun Xu
The gas dynamics under gravitational field is usually associated with the multiple scale nature due to large density variation and a wide range of local Knudsen number. It is chal-…