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The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical…

Optimization and Control · Mathematics 2015-11-30 Hung Nien , Jeffrey A. Fessler

For computational fluid dynamics (CFD), the generalized Riemann problem (GRP) solver and the gas-kinetic kinetic scheme (GKS) provide a time-accurate flux function starting from a discontinuous piecewise linear flow distributions around…

Numerical Analysis · Mathematics 2016-10-12 Liang Pan , Kun Xu , Qibing Li , Jiequan Li

This work is in the field of multi-material compressible fluid flows simulation. The proposed scheme is eulerian and related to finite volumes methods, but in a Lagrange-Remap formalism on regular orthogonal meshes. The Lagrangian scheme is…

Numerical Analysis · Mathematics 2022-08-30 Bastien Chaudet

In this paper, we propose two monolithic fully discrete finite element methods for fluid-structure interaction (FSI) based on a novel Piola-type Arbitrary Lagrangian-Eulerian (ALE) mapping. For the temporal discretization, we apply the…

Numerical Analysis · Mathematics 2026-04-09 Shuaijun Liu , Xiaoping Xie

We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…

Numerical Analysis · Mathematics 2026-04-06 Xiuhui Guo , Wei Jiang , Chunmei Su

In this paper we propose a new high order accurate space-time DG finite element scheme for the solution of the linear elastic wave equations in first order velocity-stress formulation in two and three-space dimensions on staggered…

Numerical Analysis · Mathematics 2018-05-09 Maurizio Tavelli , Michael Dumbser

This work presents algorithms for the efficient implementation of discontinuous Galerkin methods with explicit time stepping for acoustic wave propagation on unstructured meshes of quadrilaterals or hexahedra. A crucial step towards…

Numerical Analysis · Computer Science 2019-03-06 Svenja Schoeder , Katharina Kormann , Wolfgang Wall , Martin Kronbichler

The unified gas-kinetic scheme (UGKS) is becoming increasingly popular for multiscale simulations in all flow regimes. This paper provides the first analytical study on the stability of the UGKS applied to a linear kinetic model, which is…

Numerical Analysis · Mathematics 2025-05-02 Tuowei Chen , Kun Xu

In this paper, we present a thorough von Neumann stability analysis of explicit and implicit Arbitrary-Lagrangian-Eulerian (ALE) ADER discontinuous Galerkin (DG) methods on classical and degenerate spacetime geometries for hyperbolic…

Numerical Analysis · Mathematics 2026-02-11 Mauro Bonafini , Davide Torlo , Elena Gaburro

In this study, an implicit scheme for the gas-kinetic scheme (GKS) on the unstructured hybrid mesh is proposed. The Spalart-Allmaras (SA) one equation turbulence model is incorporated into the implicit gas-kinetic scheme (IGKS) to predict…

Computational Physics · Physics 2017-09-05 Dongxin Pan , Chengwen Zhong , Congshan Zhuo

In this article we present a numerical framework based on continuum models for the fluid dynamics and the CO$_2$ gas distribution in the alveolar sacs of the human lung during expiration and inspiration, including the gas exchange to the…

Numerical Analysis · Mathematics 2018-04-10 Luis J. Caucha , Stefan Frei , Obidio Rubio

The higher-order gas-kinetic scheme for solving the Navier-Stokes equations has been studied in recent years. In addition to the use of higher-order reconstruction techniques, many terms are used in the Taylor expansion of the gas…

Computational Physics · Physics 2017-04-05 Guangzhao Zhou , Kun Xu , Feng Liu

In recent developments, it has been demonstrated that the Arbitrary Lagrangian Eulerian (ALE) formulation can be utilized to improve computational efficiency, when simulating the response of structures subjected to moving loads. It is also…

Numerical Analysis · Mathematics 2026-01-15 Atul Anantheswar , Jannick Kehls , Ines Wollny , Tim Brepols , Stefanie Reese , Michael Kaliske

In this paper, a compact high-order gas-kinetic scheme (GKS) with spectral resolution will be presented and used in the simulation of acoustic and shock waves. For accurate simulation, the numerical scheme is required to have excellent…

Computational Physics · Physics 2020-12-30 Fengxiang Zhao , Xing Ji , Wei Shyy , Kun Xu

A class of high order asymptotic preserving (AP) schemes has been developed for the BGK equation in Xiong et. al. (2015) [37], which is based on the micro-macro formulation of the equation. The nodal discontinuous Galerkin (NDG) method with…

Numerical Analysis · Mathematics 2016-02-09 Tao Xiong , Jingmei Qiu

A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by…

Numerical Analysis · Mathematics 2020-12-23 Bingquan Ji , Hong-lin Liao , Yuezheng Gong , Luming Zhang

We recently derived the unified continuum and variational multiscale formulation for fluid-structure interaction (FSI) using the Gibbs free energy. Restricting our attention to vascular FSI, we now reduce this arbitrary Lagrangian-Eulerian…

Computational Physics · Physics 2022-04-06 Ingrid S. Lan , Ju Liu , Weiguang Yang , Alison L. Marsden

This paper introduces a sharp-interface approach to simulating fluid-structure interaction involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body…

A Cartesian grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the computational grid points are classified into four…

Fluid Dynamics · Physics 2015-02-17 Songze Chen , Kun Xu , Zhihui Li

New entropy stable spectral collocations schemes of arbitrary order of accuracy are developed for the unsteady 3-D Euler and Navier-Stokes equations on dynamic unstructured grids. To take into account the grid motion and deformation, we use…

Numerical Analysis · Mathematics 2019-10-23 Nail K. Yamaleev , David C. Del Rey Fernandez , Jialin Lou , Mark H. Carpenter