# A Truncation Error Estimation Scheme for the Finite Volume Method on Unstructured Meshes

## TL;DR

This paper introduces a new approximate scheme for estimating volume-based truncation errors in finite volume analysis on unstructured meshes, aiming to improve accuracy for mesh adaptation in laminar flow simulations.

## Contribution

It develops a novel truncation error estimation method based on neglected terms, offering better accuracy on unstructured meshes compared to previous approaches.

## Key findings

- The scheme provides more accurate truncation error estimates.
- It is suitable for use in mesh adaptation processes.
- The method is applicable to laminar flow simulations on unstructured meshes.

## Abstract

This work is an attempt to develop an approximate scheme for estimating the volume-based truncation errors in the finite volume analysis of laminar flows. The volume-based truncation error is the net flow error across the faces of a control volume. Unfortunately, truncation error is not a natural outcome of the finite volume solution and needs to be estimated separately. Previous works in the literature estimate truncation error using either higher order interpolation schemes, higher order discretization schemes, or neglected terms in the discretization scheme. The first two approaches become complicated on general unstructured meshes and the third approach provides inaccurate results. This work proposes a truncation error estimation scheme, which is based on the third approach, but provides more accurate results compared to the existing results in the literature. The potential application of such a truncation error estimation scheme is in mesh adaptation.