Related papers: Probabilistic Flux Limiters
Learning to integrate non-linear equations from highly resolved direct numerical simulations (DNSs) has seen recent interest for reducing the computational load for fluid simulations. Here, we focus on determining a flux-limiter for shock…
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…
Normalizing flows are objects used for modeling complicated probability density functions, and have attracted considerable interest in recent years. Many flexible families of normalizing flows have been developed. However, the focus to date…
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 idea and implementation of the first flux reconstruction…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
Numerical simulations of compressible real-fluid flows are notoriously plagued by spurious pressure oscillations arising in regions of abrupt flow variations. As a possible remedy, several numerical formulations enforce the pressure…
We theoretically investigate the effect of random fluctuations on the motion of elongated microswimmers near hydrodynamic transport barriers in externally-driven fluid flows. Focusing on the two-dimensional hyperbolic flow, we consider the…
Numerical shock instability is a complexity which may occur in supersonic simulations. Riemann solver is usually the crucial factor that affects both the computation accuracy and numerical shock stability. In this paper, several classical…
In this paper, we investigate the effect of boundary surface roughness on numerical simulations of incompressible fluid flow past a cylinder in two and three spatial dimensions furnished with slip boundary conditions. The governing…
Most fluid flow problems that are vital in engineering applications involve at least one of the following features: turbulence, shocks, and/or material interfaces. While seemingly different phenomena, these flows all share continuous…
Entropy conservation and stability of numerical methods in gas dynamics have received much interest. Entropy conservative numerical fluxes can be used as ingredients in two kinds of schemes: Firstly, as building blocks in the subcell flux…
The hydrodynamics of viscoelastic materials (for example polymer melts and solutions) presents interesting and complex phenomena, for example instabilities and turbulent flow at very low Reynolds numbers due to normal stress effects and the…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
A variety of real-world applications are modeled via hyperbolic conservation laws. To account for uncertainties or insufficient measurements, random coefficients may be incorporated. These random fields may depend discontinuously on the…
The use of flux limiters is widespread within the scientific computing community to capture shock discontinuities and are of paramount importance for the temporal integration of high-speed aerodynamics, multiphase flows, and hyperbolic…
Control systems operating in the real world face countless sources of unpredictable uncertainties. These random disturbances can render deterministic guarantees inapplicable and cause catastrophic safety failures. To overcome this, this…
Particle methods play an important role in computational fluid dynamics, but they are among the most difficult to implement and solve. The most common method is smoothed particle hydrodynamics, which is suitable for problem settings that…
This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…
This paper presents a data-driven framework for learning optimal second-order total variation diminishing (TVD) flux limiters via differentiable simulations. In our fully differentiable finite volume solvers, the limiter functions are…
In this work a simple method to enforce the positivity-preserving property for general high-order conservative schemes is proposed. The method keeps the original scheme unchanged and detects critical numerical fluxes which may lead to…