Structure-Preserving Finite Volume Scheme for Two-Phase Model

Konsep Inti

Preserving the curl-free constraint in a two-phase model with a structure-preserving finite volume scheme.

Abstrak

The content introduces a new second-order accurate finite volume scheme for a compressible barotropic two-phase model. It focuses on maintaining the curl-free constraint for the relative velocity at the discrete level. The scheme is based on a staggered grid arrangement, ensuring compatibility with gradient and curl operators. Numerical results confirm the scheme's ability to preserve the curl-free property experimentally. The content covers the governing equations, discretization methodology, and numerical results for various test cases.
Abstract:

New finite volume scheme for compressible barotropic two-phase model.
Maintaining curl-free constraint at discrete level.
Staggered grid arrangement for compatibility with operators.
Experimental confirmation of preserving curl-free property.
Introduction:

Multiphase flows complexity.
Model of Romenski for compressible barotropic two-phase flows.
Importance of preserving curl-free constraint.
Numerical Method:

Staggered grid arrangement for relative velocity.
Compatible gradient and curl operators.
Flux splitting methodology.
MUSCL-Hancock scheme for remaining terms.
Data Extraction:

"The new numerical method is based on a staggered grid arrangement where the relative velocity field is stored in the cell vertexes."
"A set of numerical results confirms this property also experimentally."
Quotations:

"The most prominent examples of involutions are the well-known divergence-free condition of the magnetic field in the Maxwell and MHD equations."
"Involution constraints generally are of little consequence at the continuous level, since solutions of the governing PDE system obey them by definition."

Statistik

The new numerical method is based on a staggered grid arrangement where the relative velocity field is stored in the cell vertexes.

Kutipan

The most prominent examples of involutions are the well-known divergence-free condition of the magnetic field in the Maxwell and MHD equations.
Involution constraints generally are of little consequence at the continuous level, since solutions of the governing PDE system obey them by definition.

Wawasan Utama Disaring Dari

An exactly curl-free finite-volume scheme for a hyperbolic compressible barotropic two-phase model

by Laur... pada arxiv.org 03-28-2024

https://arxiv.org/pdf/2403.18724.pdf

Pertanyaan yang Lebih Dalam

How does the new finite volume scheme compare to other numerical methods for two-phase models

The new finite volume scheme presented in the context for two-phase models offers a unique advantage in that it exactly preserves the curl-free constraint at the discrete level. This is a crucial property for models with a curl-free constraint, as it ensures the numerical solution remains physically relevant and accurate. By storing the relative velocity field in the cell vertices and using compatible gradient and curl operators, the scheme maintains the structural property of the model. This sets it apart from other numerical methods that may not explicitly preserve such constraints, leading to potential errors and inaccuracies in the solution. The use of staggered grids and structure-preserving discretizations in this scheme enhances its accuracy and reliability in capturing the dynamics of compressible barotropic two-phase flows.

What are the implications of not preserving the curl-free constraint in the discrete level

Not preserving the curl-free constraint at the discrete level can have significant implications for the accuracy and reliability of the numerical solution in two-phase models. The curl-free constraint for the relative velocity field is an intrinsic property of the model, and violating this constraint can lead to unphysical solutions. Inaccuracies in maintaining the curl-free property can result in numerical instabilities, incorrect flow patterns, and overall unreliable results. Additionally, the violation of the curl-free constraint may lead to the loss of important physical information and the introduction of errors that can propagate throughout the simulation. Therefore, ensuring the exact preservation of the curl-free constraint at the discrete level is essential for obtaining meaningful and accurate results in simulations of compressible barotropic two-phase flows.

How can the concept of involutions be applied to other areas of physics and continuum mechanics

The concept of involutions, as seen in the context of the curl-free constraint in the two-phase model, can be applied to various areas of physics and continuum mechanics where differential constraints play a crucial role. In electromagnetism, the divergence-free condition of the magnetic field in Maxwell's equations is a well-known example of an involution. Similarly, in solid mechanics, the curl-free property of the deformation gradient is another instance of an involution constraint. These involutions are essential for maintaining the physical consistency and integrity of the governing equations. By developing numerical methods that preserve these differential constraints at the discrete level, researchers can ensure the accuracy and reliability of simulations in various fields, including fluid dynamics, electromagnetism, and solid mechanics. The application of structure-preserving discretizations and compatible operators to maintain involutions can lead to more robust and physically meaningful numerical solutions across different areas of physics and continuum mechanics.