相关论文: Two variants of the MCV3 scheme

In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…

Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality…

This paper proposes a novel first-order and a novel second-order fully discrete virtual element schemes based on the scalar auxiliary variable method for the three dimensional inductionless magnetohydrodynamics problem. The backward Eular…

In this paper, we develop novel numerical methods based on the Multi-Point Flux Approximation (MPFA) method to solve the degenerated partial differential equation (PDE) arising from pricing two-assets options. The standard MPFA is used as…

The higher-order gas-kinetic scheme for solving the Navier-Stokes equations has been studied in recent years. In addition to the use of higher-order reconstruction techniques, many terms are used in the Taylor expansion of the gas…

We present a practical cell-centred volume-of-fluid method developed within a pure Eulerian setting for the simulation of compressible solid-fluid problems. The method builds on a previously published diffuse-interface Godunov-type scheme…

In this paper, we present a fully local second-order upwind scheme, applicable on generic meshes. This is done by hybridisation, which is achieved by introducing unknowns on each edge of the mesh. By doing so, fluxes only depend on values…

We adapt a troubled-cell indicator from discontinuous Galerkin (DG) methods to finite volume methods (FVM) with MUSCL reconstruction and using a novel monotonicity parameter show there is a trade-off between convergence and quality of the…

Over the past decades, the volume-of-fluid (VOF) method has been the method of choice for simulating atomization processes, owing to its unique ability to discretely conserve mass. Current state-of-the-art VOF methods, however, rely on the…

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…

This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…

A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid. In this paper, two kinds of moments, i.e. point values (PV moment) at cell boundaries and…

A second-order-accurate finite volume method, hybridized by blending an extended double-flux algorithm and a traditionally conservative scheme, is developed. In this scheme, hybrid convective fluxes as well as hybrid interpolation…

We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. We modify the classical algorithm by introducing a new…

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,…

Cylindrical coordinates are often used in computational fluid dynamics, in particular, when one considers gas flow accreting onto a central object. Although the cylindrical coordinates have several advantages in describing rotation, they…

To ensure the discrete maximum principle or solution positivity in finite volume schemes, diffusive flux is sometimes discretized as a conical combination of finite differences. Such a combination may be impossible to construct along…

Mathematical Programs with Vanishing Constraints (MPVCs) are a notoriously challenging class of problems owing to their lack of constraint qualification. Therefore, to tackle these problems, relaxation-based approaches are typically used.…

We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global…

Two finite volume methods are derived and applied to the solution of problems of incompressible flow. In particular, external inviscid flows and boundary-layer flows are examined. The firstmethod analyzed is a cell-centered finite volume…