Related papers: On Godunov-type finite volume methods for seismic …
Machine learning techniques are being used as an alternative to traditional numerical discretization methods for solving hyperbolic partial differential equations (PDEs) relevant to fluid flow. Whilst numerical methods are higher fidelity,…
To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the…
The aim of the present paper is to provide a comparison between several finite-volume methods of different numerical accuracy: second-order Godunov method with PPM interpolation and high-order finite-volume WENO method. The results show…
Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems.…
The aim of this work is to construct efficient finite volume schemes for the numerical study of sediment transport in shallow water, in the framework of the Exner model.In most cases, the velocity related to the sediment is much lower that…
We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular we consider a KdV-BBM type equation. Explicit and IMEX Runge-Kutta type methods are used for time…
In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with appropriate predictor-corrector method to achieve higher resolution. The underlying finite…
In this paper, an upwind GFDM is developed for the coupled heat and mass transfer problems in porous media. GFDM is a meshless method that can obtain the difference schemes of spatial derivatives by using Taylor expansion in local node…
This paper presents a sharp free surface method for fully nonlinear flow of two immiscible phases for wave propagation problems in the Finite Volume framework. The method resolves a sharp interface between two phases by combining the…
This work outlines a new three-dimensional diffuse interface finite volume method for the simulation of multiple solid and fluid components featuring large deformations, sliding and void opening. This is achieved by extending an existing…
Seismic inversion is a core problem in geophysical exploration, where traditional methods suffer from high computational costs and are susceptible to initial model dependence. In recent years, deep generative model-based seismic inversion…
We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…
Simple modifications for higher-order Godunov-type difference schemes are presented which allow for accurate advection of multi-fluid flows in hydrodynamic simulations. The constraint that the sum of all mass fractions has to be equal to…
Purpose: This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using numerical benchmarks. Design/methodology/approach:…
We introduce a new Eulerian simulation framework for liquid animation that leverages both finite element and finite volume methods. In contrast to previous methods where the whole simulation domain is discretized either using the finite…
Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems.…
Computational fluid dynamics (CFD) simulation is an irreplaceable modelling step in many engineering designs, but it is often computationally expensive. Some graph neural network (GNN)-based CFD methods have been proposed. However, the…
When fully conservative methods are used to simulate transcritical flow, spurious pressure oscillations and numerical instability are generated. The strength and speed of propagation of shock waves cannot be represented correctly using a…
High-order accurate summation-by-parts (SBP) finite difference (FD) methods constitute efficient numerical methods for simulating large-scale hyperbolic wave propagation problems. Traditional SBP FD operators that approximate first-order…
We introduce a fluid dynamics algorithm that performs with nearly spectral accuracy, but uses finite-differences instead of FFTs to compute gradients and thus executes 10 times faster. The finite differencing is not based on a high-order…