scholarly journals A reconstructed discontinuous Galerkin method for compressible flows on moving curved grids

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Chuanjin Wang ◽  
Hong Luo
Keyword(s):  
Discontinuous Galerkin ◽  
Compressible Flows ◽  
Interpolation Method ◽  
Temporal Integration ◽  
Arbitrary Lagrangian Eulerian ◽  
Boundary Problems ◽  
Mesh Motion ◽  
Ale Formulation ◽  
Time Dependent Domain ◽  
The Right

AbstractA high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for compressible inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation on moving and deforming unstructured curved meshes. Taylor basis functions in the rDG method are defined on the time-dependent domain, where the integration and computations are performed. The Geometric Conservation Law (GCL) is satisfied by modifying the grid velocity terms on the right-hand side of the discretized equations at Gauss quadrature points. A radial basis function (RBF) interpolation method is used for propagating the mesh motion of the boundary nodes to the interior of the mesh. A third order Explicit first stage, Single Diagonal coefficient, diagonally Implicit Runge-Kutta scheme (ESDIRK3) is employed for the temporal integration. A number of benchmark test cases are conducted to assess the accuracy and robustness of the rDG-ALE method for moving and deforming boundary problems. The numerical experiments indicate that the developed rDG method can attain the designed spatial and temporal orders of accuracy, and the RBF method is effective and robust to avoid excessive distortion and invalid elements near moving boundaries.

scholarly journals A Reconstructed Discontinuous Galerkin Method for Compressible Flows on Moving Curved Grids

2020 ◽  
Author(s):  
Hong Luo ◽  
Chuanjin Wang
Keyword(s):  
Discontinuous Galerkin ◽  
Compressible Flows ◽  
Interpolation Method ◽  
Temporal Integration ◽  
Arbitrary Lagrangian Eulerian ◽  
Boundary Problems ◽  
Mesh Motion ◽  
Ale Formulation ◽  
Time Dependent Domain ◽  
The Right

Abstract A high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for compressible inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation on moving and deforming unstructured curved meshes. Taylor basis functions in the rDG method are defined on the time-dependent domain, where the integration and computations are performed. The Geometric Conservation Law (GCL) is satisfied by modifying the grid velocity terms on the right-hand side of the discretized equations at Gauss quadrature points. A radial basis function (RBF) interpolation method is used for propagating the mesh motion of the boundary nodes to the interior of the mesh. A third order Explicit first stage, Single Diagonal coefficient, diagonally Implicit Runge-Kutta scheme (ESDIRK3) is employed for the temporal integration. A number of benchmark test cases are conducted to assess the accuracy and robustness of the rDG-ALE method for moving and deforming boundary problems. The numerical experiments indicate that the developed rDG method can attain the designed spatial and temporal orders of accuracy, and the RBF method is effective and robust to avoid excessive distortion and elements near moving boundaries.

scholarly journals A Reconstructed Discontinuous Galerkin Method for Compressible Flows on Moving Curved Grids

2020 ◽  
Author(s):  
Chuanjin Wang ◽  
Hong Luo
Keyword(s):  
Discontinuous Galerkin ◽  
Compressible Flows ◽  
Interpolation Method ◽  
Temporal Integration ◽  
Arbitrary Lagrangian Eulerian ◽  
Boundary Problems ◽  
Mesh Motion ◽  
Ale Formulation ◽  
Time Dependent Domain ◽  
The Right

Abstract A high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for compressible inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation on moving and deforming unstructured curved meshes. Taylor basis functions in the rDG method are defined on the time-dependent domain, where the integration and computations are performed. The Geometric Conservation Law (GCL) is satisfied by modifying the grid velocity terms on the right-hand side of the discretized equations at Gauss quadrature points. A radial basis function (RBF) interpolation method is used for propagating the mesh motion of the boundary nodes to the interior of the mesh. A third order Explicit first stage, Single Diagonal coefficient, diagonally Implicit Runge-Kutta scheme (ESDIRK3) is employed for the temporal integration. A number of benchmark test cases are conducted to assess the accuracy and robustness of the rDG-ALE method for moving and deforming boundary problems. The numerical experiments indicate that the developed rDG method can attain the designed spatial and temporal orders of accuracy, and the RBF method is effective and robust to avoid excessive distortion and elements near moving boundaries.

scholarly journals A High-Order Method for Weakly Compressible Flows

2017 ◽  
Vol 22 (4) ◽  
pp. 1150-1174 ◽  
Author(s):  
Klaus Kaiser ◽  
Jochen Schütz
Keyword(s):  
Euler Equations ◽  
Discontinuous Galerkin ◽  
Compressible Flows ◽  
Temporal Integration ◽  
Reference Solution ◽  
Order Method ◽  
Asymptotic Preserving ◽  
High Order Method ◽  
Weakly Compressible ◽  
Isentropic Euler Equations

AbstractIn this work, we introduce an IMEX discontinuous Galerkin solver for the weakly compressible isentropic Euler equations. The splitting needed for the IMEX temporal integration is based on the recently introducedreference solutionsplitting [32, 52], which makes use of theincompressiblesolution. We show that the overall method isasymptotic preserving. Numerical results show the performance of the algorithm which is stable under a convective CFL condition and does not show any order degradation.

A Consistent Implementation of Inelastic Material Models into Steady State Rolling

2016 ◽  
Vol 44 (3) ◽  
pp. 174-190 ◽  
Author(s):  
Mario A. Garcia ◽  
Michael Kaliske ◽  
Jin Wang ◽  
Grama Bhashyam
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Viscoelastic Material ◽  
Rolling Contact ◽  
Arbitrary Lagrangian Eulerian ◽  
Ale Formulation ◽  
Inelastic Material ◽  
Material Formulation ◽  
Steady State Rolling ◽  
Efficient Alternative

ABSTRACT Rolling contact is an important aspect in tire design, and reliable numerical simulations are required in order to improve the tire layout, performance, and safety. This includes the consideration of as many significant characteristics of the materials as possible. An example is found in the nonlinear and inelastic properties of the rubber compounds. For numerical simulations of tires, steady state rolling is an efficient alternative to standard transient analyses, and this work makes use of an Arbitrary Lagrangian Eulerian (ALE) formulation for the computation of the inertia contribution. Since the reference configuration is neither attached to the material nor fixed in space, handling history variables of inelastic materials becomes a complex task. A standard viscoelastic material approach is implemented. In the inelastic steady state rolling case, one location in the cross-section depends on all material locations on its circumferential ring. A consistent linearization is formulated taking into account the contribution of all finite elements connected in the hoop direction. As an outcome of this approach, the number of nonzero values in the general stiffness matrix increases, producing a more populated matrix that has to be solved. This implementation is done in the commercial finite element code ANSYS. Numerical results confirm the reliability and capabilities of the linearization for the steady state viscoelastic material formulation. A discussion on the results obtained, important remarks, and an outlook on further research conclude this work.

scholarly journals A linear-elasticity-based mesh moving method with no cycle-to-cycle accumulated distortion

2021 ◽  
Author(s):  
Patrícia Tonon ◽  
Rodolfo André Kuche Sanches ◽  
Kenji Takizawa ◽  
Tayfun E. Tezduyar
Keyword(s):  
Linear Elasticity ◽  
Solid Surfaces ◽  
Moving Mesh ◽  
Test Case ◽  
Half Cycle ◽  
Arbitrary Lagrangian Eulerian ◽  
Interface Motion ◽  
Mesh Motion ◽  
Ale Methods ◽  
Moving Mesh Methods

AbstractGood mesh moving methods are always part of what makes moving-mesh methods good in computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) and arbitrary Lagrangian–Eulerian (ALE) methods, enable mesh-resolution control near solid surfaces and thus high-resolution representation of the boundary layers. Mesh moving based on linear elasticity and mesh-Jacobian-based stiffening (MJBS) has been in use with the ST and ALE methods since 1992. In the MJBS, the objective is to stiffen the smaller elements, which are typically placed near solid surfaces, more than the larger ones, and this is accomplished by altering the way we account for the Jacobian of the transformation from the element domain to the physical domain. In computing the mesh motion between time levels $$t_n$$ t n and $$t_{n+1}$$ t n + 1 with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at $$t_n$$ t n . While this option works well for most problems, because the method is path-dependent, it involves cycle-to-cycle accumulated mesh distortion. The back-cycle-based mesh moving (BCBMM) method, introduced recently with two versions, can remedy that. In the BCBMM, there is no cycle-to-cycle accumulated distortion. In this article, for the first time, we present mesh moving test computations with the BCBMM. We also introduce a version we call “half-cycle-based mesh moving” (HCBMM) method, and that is for computations where the boundary or interface motion in the second half of the cycle consists of just reversing the steps in the first half and we want the mesh to behave the same way. We present detailed 2D and 3D test computations with finite element meshes, using as the test case the mesh motion associated with wing pitching. The computations show that all versions of the BCBMM perform well, with no cycle-to-cycle accumulated distortion, and with the HCBMM, as the wing in the second half of the cycle just reverses its motion steps in the first half, the mesh behaves the same way.

scholarly journals A stable method for 4D CT-based CFD simulation in the right ventricle of a TGA patient

2020 ◽  
Vol 35 (5) ◽  
pp. 315-324
Author(s):  
Yuri Vassilevski ◽  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Victoria Salamatova ◽  
...  
Keyword(s):  
Right Ventricle ◽  
Cfd Simulation ◽  
Fluid Motion ◽  
4D Ct ◽  
Post Surgery ◽  
Surgery Patient ◽  
Time Dependent Domain ◽  
Flow Domain ◽  
The Right ◽  
Dependent Domain

AbstractThe paper discusses a stabilization of a finite element method for the equations of fluid motion in a time-dependent domain. After experimental convergence analysis, the method is applied to simulate a blood flow in the right ventricle of a post-surgery patient with the transposition of the great arteries disorder. The flow domain is reconstructed from a sequence of 4D CT images. The corresponding segmentation and triangulation algorithms are also addressed in brief.

Iterative method for solving fully-coupled fluid solid systems

2010 ◽  
pp. 653-670
Author(s):  
Elisabeth Longatte
Keyword(s):  
Stokes Equations ◽  
Cross Flow ◽  
Elastic Cylinder ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Ale Formulation ◽  
Volume Method ◽  
Fully Coupled ◽  
Solid System

This work is concerned with the modelling of the interaction of a fluid with a rigid or a flexible elastic cylinder in the presence of axial or cross-flow. A partitioned procedure is involved to perform the computation of the fully-coupled fluid solid system. The fluid flow is governed by the incompressible Navier-Stokes equations and modeled by using a fractional step scheme combined with a co-located finite volume method for space discretisation. The motion of the fluid domain is accounted for by a moving mesh strategy through an Arbitrary Lagrangian-Eulerian (ALE) formulation. Solid dyncamics is modeled by a finite element method in the linear elasticity framework and a fixed point method is used for the fluid solid system computation. In the present work two examples are presented to show the method robustness and efficiency.

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