trixi-framework/Trixi.jl

Implement mortar correction procedure from Chan et al.

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#195 opened on Oct 1, 2020

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enhancementgood first issuepossible student project

Description

The projection mortar operator applied to the DG approximation with LGL nodes is stable for upwind surface fluxes but is unstable for central surface fluxes. This is due to the presence of positive eigenvalues in the operator. The recent mortar correction described by Jesse (https://arxiv.org/abs/2005.03237) fixes this issue, allowing one to use central fluxes at the mortars with LGL nodes.

Contributor guide

Tech stack
None
Domain
backendperformance
Issue type
feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
5
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
over 1 week
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
stale
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
needs investigation
Prerequisites
Discontinuous Galerkin methodsMortar operatorsJulia programmingTrixi.jl structure
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
15
Research direction
Implement the mortar correction algorithm described in Chan et al. (arXiv:2005.03237) to stabilize central fluxes at mortars with LGL nodes. This requires locating the existing mortar implementation in Trixi.jl (likely in src/ or similar) and modifying the projection operator to incorporate the correction. After implementation, validate with numerical tests to ensure stability.