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The linear Navier-Stokes-Fourier (NSF) constitutive relations are capable of simulating the near-continuum flows, but fail in description of those flows which are removed far away from local equilibrium. In this paper, a diatomic nonlinear…
In this study, the multiple solutions of Nonlinear Coupled Constitutive Relation (NCCR) model are firstly observed and a way for identifying the physical solution is proposed. The NCCR model proposed by Myong is constructed from the…
The inability of the Navier-Stokes-Fourier equations to capture rarefaction effects motivates us to adopt the extended hydrodynamic equations. In the present work, a hydrodynamic model, which consists of the conservation laws closed with…
Provable nonlinear stability bounds the discrete approximation and ensures that the discretization does not diverge. For high-order methods, discrete nonlinear stability and entropy stability, have been successfully implemented for…
Classical continuum-based liquid vapour phase-change models typically assume continuity of temperature at phase interfaces along with a relation which describes the rate of evaporation at the interface (Hertz-Knudsen-Schrage, for example).…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
Three-dimensional (3D) high-speed compressible flow is a typical nonlinear, nonequilibrium, and multiscale complex flow. Traditional fluid mechanics models, based on the quasi-continuum assumption and near-equilibrium approximation, are…
For increasingly rarefied flowfields, the Navier-Stokes (NS) equations lose accuracy partially due to the single temperature approximation. To overcome this barrier, a continuum multi-temperature model based on the Bhatnagar-Gross-Krook…
Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…
We analyze the representation of viscous stresses in the one-fluid formulation of the two-phase Navier-Stokes equations, the model on which all computational approaches making use of a fixed mesh to discretize the flow field are grounded.…
The fluid flow transport and hydrodynamic problems often take the form of hyperbolic systems of conservation laws. In this work we will present a new scheme of finite volume methods for solving these evolution equations. It is a family of…
Typical multispecies compressible Navier-Stokes computations employ conservative equations for mass fraction transport. Upwind discretisations of these governing equations produce spurious pressure oscillations at diffuse contact surfaces…
Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article blood is treated as an…
The accurate and efficient modeling of granular flows and their interactions with external bodies is an open research problem. Continuum methods can be used to capture complexities neglected by terramechanics models without the…
This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation…
The accuracy and stability of implicit CFD codes are frequently impaired by the decoupling between variables, which can ultimately lead to numerical divergence. Coupled solvers, which solve all the governing equations simultaneously, have…
The well-known Navier--Stokes--Fourier equations of fluid dynamics are, in general, not adequate for describing rarefied gas flows. Moreover, while the Stokes equations -- a simplified version of the Navier--Stokes--Fourier equations -- are…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…
This report summarizes the major progresses to develop the dynamic core for next-generation atmospherical model for both numerical weather prediction and climate simulation. The numerical framework is based on a general formulation,…
A computationally accurate and efficient numerical method under a unified framework is crucial to various multi-scale scientific and engineering problems. So far, many numerical methods have encountered various challenges in efficiently…