相关论文: An Efficient Steady-State Solver for Microflows wi…

In this paper we present a genuinely two-dimensional HLLC Riemann solver. On logically rectangular meshes, it accepts four input states that come together at an edge and outputs the multi-dimensionally upwinded fluxes in both directions.…

Modeling transition-continuum hypersonic flows poses significant challenges due to thermodynamic nonequilibrium and the associated breakdown of the continuum assumption. Standard continuum models such as the Navier-Stokes equations are…

A new lattice Boltzmann (LB) model is introduced, based on a regularization of the pre-collision distribution functions in terms of the local density, velocity, and momentum flux tensor. The model dramatically improves the precision and…

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…

Stellar convection poses two main gargantuan challenges for astrophysical fluid solvers: low-Mach number flows and minuscule perturbations over steeply stratified hydrostatic equilibria. Most methods exhibit excessive numerical diffusion…

We present a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds with high weak order of accuracy. In opposition to the popular approach with projection methods,…

Recently it was discovered that altering the shape of the meta stable and unstable branches of an equation of state (EOS) can greatly improve the numerical accuracy of liquid and gas densities in the pseudopotential method. Inspired by this…

Molecular dynamics simulations are indispensable for exploring the behavior of atoms and molecules. Grounded in quantum mechanical principles, quantum molecular dynamics provides high predictive power but its computational cost is dominated…

We investigate the use of reduced-order modelling to run discrete element simulations at higher speeds. Taking a data-driven approach, we run many offline simulations in advance and train a model to predict the velocity field from the mass…

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…

The structural properties of mechanical metamaterials are typically studied with two-scale methods based on computational homogenization. Because such materials have a complex microstructure, enriched schemes such as second-order…

In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-grid…

Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…

We propose to accelerate a high order discontinuous Galerkin solver using neural networks. We include a corrective forcing to a low polynomial order simulation to enhance its accuracy. The forcing is obtained by training a deep fully…

In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features…

Machine learning methods, such as diffusion models, are widely explored as a promising way to accelerate high-fidelity fluid dynamics computation via a super-resolution process from faster-to-compute low-fidelity input. However, existing…

In this work, the exact reproduction of a moving-water steady flow via the numerical solution of the one-dimensional shallow water equations is studied. A new scheme based on a modified version of the HLLEM approximate Riemann solver…

A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for high speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara[Phys. Rev. E 69, 056702 (2004)]. The convection…

In this paper we present a novel pressure-based semi-implicit finite volume solver for the equations of compressible ideal, viscous and resistive magnetohydrodynamics (MHD). The new method is conservative for mass, momentum and total energy…

We survey a number of moment hierarchies and test their performances in computing one-dimensional shock structures. It is found that for high Mach numbers, the moment hierarchies are either computationally expensive or hard to converge,…