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Seismic imaging of the mantle has revealed large and small scale heterogeneities in the lower mantle; specifically structures known as large low shear velocity provinces (LLSVP) below Africa and the South Pacific. Most interpretations…

We present a new method for simulating incompressible immiscible two-phase flow in porous media. The semi-implicit method decouples the wetting phase pressure and saturation equations. The equations are discretized using a hybridizable…

Computational Engineering, Finance, and Science · Computer Science 2018-02-19 Maurice S. Fabien , Matthew G. Knepley , Beatrice M. Riviere

We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…

Numerical Analysis · Mathematics 2020-01-08 Hong Xiao , Eky Febrianto , Qiaoling Zhang , Fehmi Cirak

Field inversion and machine learning are implemented in this study to describe three-dimensional separation flow around an axisymmetric hill and augment the Spart-Allmaras model. The discrete adjoint method is used to solve the field…

Fluid Dynamics · Physics 2022-07-29 Chongyang Yan , Yufei Zhang , Haixin Chen

We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime…

Numerical Analysis · Mathematics 2023-02-28 B. J. Gross , N. Trask , P. Kuberry , P. J. Atzberger

Development of a two-phase incompressible solver for magnetic flows in the magnetostatic case is presented. The proposed numerical toolkit couples the Navier-Stokes equations of hydrodynamics with Maxwell's equations of electromagnetism to…

Fluid Dynamics · Physics 2024-06-04 Paria Makaremi-Esfarjani , Andrew J. Higgins , Alireza Najafi-Yazdi

The high-order numerical solution of the non-linear shallow water equations (and of hyperbolic systems in general) is susceptible to unphysical Gibbs oscillations that form in the proximity of strong gradients. The solution to this problem…

Numerical Analysis · Mathematics 2016-07-18 Simone Marras , Michal A. Kopera , Emil M. Constantinescu , Jenny Suckale , Francis X. Giraldo

In this work we consider Runge-Kutta discontinuous Galerkin methods (RKDG) for the solution of hyperbolic equations enabling high order discretization in space and time. We aim at an efficient implementation of DG for Euler equations on…

Numerical Analysis · Mathematics 2021-04-12 M. Siebenborn , V. Schulz , S. Schmidt

We propose a new arbitrary high order accurate semi-implicit space-time discontinuous Galerkin (DG) method for the solution of the two and three dimensional compressible Euler and Navier-Stokes equations on staggered unstructured curved…

Numerical Analysis · Mathematics 2017-05-24 Maurizio Tavelli , Michael Dumbser

We present a new high-resolution, non-oscillatory semi-discrete central-upwind scheme for one-dimensional two-layer shallow-water flows with friction and entrainment along channels with arbitrary cross sections and bottom topography. These…

Numerical Analysis · Mathematics 2021-04-08 Gerardo Hernandez-Duenas , Jorge Balbas

This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network…

Gas-particle flows are commonly simulated through two-fluid model at industrial-scale. However, these simulations need very fine grid to have accurate flow predictions, which is prohibitively demanding in terms of computational resources.…

The active flux (AF) method is a compact high-order finite volume method that simultaneously evolves cell averages and point values at cell interfaces. Within the method of lines framework, the existing Jacobian splitting-based point value…

Numerical Analysis · Mathematics 2025-03-21 Junming Duan , Wasilij Barsukow , Christian Klingenberg

In this article we present a novel staggered semi-implicit hybrid finite-volume/finite-element (FV/FE) method for the resolution of weakly compressible flows in two and three space dimensions. The pressure-based methodology introduced in…

Numerical Analysis · Mathematics 2020-06-16 A. Bermúdez , S. Busto , M. Dumbser , J. L. Ferrín , L. Saavedra , M. E. Vázquez-Cendón

The present paper addresses the development and implementation of the first high-order Flux Reconstruction (FR) solver for high-speed flows within the open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics)…

Computational Physics · Physics 2019-07-24 Ray Vandenhoeck , Andrea Lani

Accurate and efficient simulation of fluid-structure interaction (FSI) problems remains a central challenge in computational physics. High-order discontinuous Galerkin (DG) methods offer low numerical errors and excellent scalability on…

Fluid Dynamics · Physics 2025-12-08 Yingjie Xia , Stefano Colombo , David Huergo , Jiaqing Kou , Yuting Dai , Esteban Ferrer

High-order discontinuous Galerkin (DG) methods equipped with subcell finite-volume (FV) limiters provide an efficient framework for the simulation of nonlinear hyperbolic balance laws featuring shocks and complex flow structures. However,…

Numerical Analysis · Mathematics 2026-05-05 Andrés M. Rueda-Ramírez , Patrick Ersing , Andrew R. Winters , Gregor J. Gassner

This paper studies the active flux (AF) methods for two-dimensional hyperbolic conservation laws, focusing on the flux vector splitting (FVS) for the point value update and bound-preserving (BP) limitings, which is an extension of our…

Numerical Analysis · Mathematics 2024-11-05 Junming Duan , Wasilij Barsukow , Christian Klingenberg

We develop a family of $H(\mathrm{div})$-conforming hybridizable discontinuous Galerkin methods for the steady Stokes equations based on BDM and RT velocity spaces with either discontinuous or continuous hybrid traces. In contrast to our…

Numerical Analysis · Mathematics 2026-04-23 Gang Chen , Wenyi Liu , Yangwen Zhang

The $L^2$ gradient flow of the Ginzburg-Landau free energy functional leads to the Allen Cahn equation that is widely used for modeling phase separation. Machine learning methods for solving the Allen-Cahn equation in its strong form suffer…

Machine Learning · Computer Science 2025-03-27 Revanth Mattey , Susanta Ghosh