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A treatment of direct simulation Monte Carlo method (DSMC) as a Markov process with a master equation is given and the corresponding master equation is derived. A hierarchy of equations for the reduced probability distributions is derived…
Short-fiber-reinforced composites (SFRC) are high-performance engineering materials for lightweight structural applications in the automotive and electronics industries. Typically, SFRC structures are manufactured by injection molding,…
In this work, we present an upscaled model for mixed dimensional coupled flow problem in fractured porous media. We consider both embedded and discrete fracture models (EFM and DFM) as fine scale models which contain coupled system of…
Multilevel Monte Carlo (MLMC) reduces the total computational cost of financial option pricing by combining SDE approximations with multiple resolutions. This paper explores a further avenue for reducing cost and improving power efficiency…
To figure out the stability issues brought by renewable energy sources (RES) with non-Gaussian uncertainties in isolated microgrids, this paper proposes a chance constrained stability constrained optimal power flow (CC-SC-OPF) model.…
A cost-effective multi-objective shape optimization strategy is proposed for high-Reynolds number flows involving complex phenomena such as boundary layer transition, shock-wave interactions, and turbulent wakes. These processes are poorly…
Rapid and accurate urban wind field prediction is essential for modeling particle transport in emergency scenarios. Traditional Computational Fluid Dynamics (CFD) approaches are too slow for real-time applications, necessitating surrogate…
Bayesian formulations of inverse problems are attractive for their ability to incorporate prior knowledge and update probabilistic models as new data become available. Markov chain Monte Carlo (MCMC) methods sample posterior probability…
A new approach to simulating rotational cooling using a direct simulation Monte Carlo (DSMC) method is described and applied to the rotational cooling of ammonia seeded into a helium supersonic jet. The method makes use of ab initio…
In the quest for advanced propulsion and power-generation systems, high-fidelity simulations are too computationally expensive to survey the desired design space, and a new design methodology is needed that combines engineering physics,…
In this work, the Navier-Stokes (NS) solver is combined with the Direct simulation Monte Carlo (DSMC) solver in a direct way, under the wave-particle formulation [J. Comput. Phys. 401, 108977 (2020)]. Different from the classical domain…
Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of compressible two-component flow, and propose a heterogeneous…
Discrete unified gas-kinetic scheme (DUGKS) is a multi-scale numerical method for flows from continuum limit to free molecular limit, and is especially suitable for the simulation of multi-scale flows, benefiting from its multi-scale…
We present a novel reduced-order fluid simulation technique leveraging Dynamic Mode Decomposition (DMD) to achieve fast, memory-efficient, and user-controllable subspace simulation. We demonstrate that our approach combines the strengths of…
The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop-on-demand (DoD)…
Aeroelasticity in the transonic regime is challenging because of the strongly nonlinear phenomena involved in the formation of shock waves and flow separation. In this work, we introduce a computationally efficient framework for accurate…
Estimating the probabilities of rare failure events is a key challenge in the reliability analysis of physical systems. Subset simulation (SS) is a very popular adaptive Monte Carlo method for this problem. In SS, the small failure…
A multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It is based on the introduction of two different surrogate models and an adaptive on-the-fly switching. The two concurrent surrogates are built…
The design of structures and vehicles subject to fluid-structure interaction (FSI) often requires high-fidelity coupled analysis. While the design variables pertain to the structure, the computational cost is dominated by the fluid solver,…
Hydrogen fuel cells are a key technology in the transition toward carbon-neutral energy systems, offering clean power with water as the only byproduct. Microfluidic fuel cells, which operate at the microliter scale, are an emerging variant…