# A multi-prediction implicit scheme for steady state solutions of gas flow in all flow regimes

## TL;DR

This paper introduces a multiscale implicit scheme with multiple macroscopic predictions for steady gas flow solutions across all regimes, significantly accelerating convergence especially in continuum flows.

## Contribution

The paper develops a novel multiscale implicit method with multiple macroscopic predictions within the DVM framework, enhancing convergence speed in continuum flow regimes.

## Key findings

- Method is one order of magnitude faster than previous schemes in continuum flows.
- Effective across all flow regimes with improved convergence.
- Utilizes a multiscale flux similar to DUGKS.

## Abstract

An implicit multiscale method with multiple macroscopic prediction for steady state solutions of gas flow in all flow regimes is presented. The method is based on the finite volume discrete velocity method (DVM) framework. At the cell interface a multiscale flux with a construction similar to discrete unified gas-kinetic scheme (DUGKS) is adopted. The idea of the macroscopic variable prediction is further developed and a multiple prediction structure is formed. A prediction scheme is constructed to give a predicted macroscopic variable based on the macroscopic residual, and the convergence is accelerated greatly in the continuum flow regime. Test cases show the present method is one order of magnitude faster than the previous implicit multiscale scheme in the continuum flow regime.