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• A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids

  H. Luo, J. Baum, R. Lohner

  Journal of Computational Physics (2006). Vol. 211 (2), pp. 767-783

  
  

  Abstract

      A p-multigrid (p = polynomial degree) discontinuous Galerkin method is presented for the solution of the compressible Euler equations on unstructured grids. The method operates on a sequence of solution approximations of different polynomial orders. A distinct feature of this p-multigrid method is to use different time integration schemes on different approximation levels, resulting in an accurate, fast, and low memory method that can be used to accelerate the convergence of the Euler equations to a steady state for discontinuous Galerkin methods. The developed method is used to compute the compressible flows for a variety of test problems on unstructured grids. The numerical results obtained strongly indicate the order independent property of this p-multigrid method. An overall speed-up factor more than one order of magnitude for both second- and third-order solutions of all test cases in comparison with the explicit method is demonstrated.

  Abstract
      A p-multigrid (p = polynomial degree) discontinuous Galerkin method is presented for the solution of the compressible Euler [...]

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• Electromagnetic scattering calculations using a finite—element solver for the Maxwell equations

  R. DeVore, R. Lohner, J. Ambrosiano

  (1991). Advances in the Free-Lagrange Method Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method. Lecture Notes in Physics, vol 395. Springer, Berlin, Heidelberg

  
  

  Abstract

  We describe a pair of finite-element codes which use unstructured meshes to solve the time-dependent Maxwell equations, with particular emphasis on their application to electromagnetic scattering problems. A two-step, flux-corrected transport scheme is used to effect the time integration, while the spatial structure of the field is determined by a Galerkin procedure. The basis functions are piecewise-linear on three-noded triangles in two dimensions and four-noded tetrahedra in three. For the periodic scattering problems with which we are presently concerned, adaptive remeshing is a convenient and powerful method for improving the quality of the solutions. Results for the analytically tractable case of scattering by a perfectly conducting circular cylinder are used to illustrate the performance of the codes.

  Abstract
  We describe a pair of finite-element codes which use unstructured meshes to solve the time-dependent Maxwell equations, with particular emphasis on their application to electromagnetic [...]

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• Electromagnetic particle codes on unstructured grids

  J. Ambrosiano, S. Brandon, R. Lohner

  (1991). Advances in the Free-Lagrange Method Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method. Lecture Notes in Physics, vol 395. Springer, Berlin, Heidelberg

  
  

  Abstract

  The most widely used computational model of collisionless plasmas is the Lagrangian-Eulerian hybrid technique known as particle-in-cell or PIC. In the electromagnetic version, Maxwell's equations are solved on an Eulerian grid and electromagnetic forces are interpolated form the grid to particle locations. Particles are then moved in Lagrangian fashion while their currents are interpolated back onto the grid to provide sources for the fields on the next cycle. There are many applications where one needs to model plasmas and electromagnetic waves inside regions of complicated shape. Traditional methods for solving Maxwell's equations employ finite differences on regular grids to replace differential operators. These methods are awkward for complicated boundary shapes, often replacing smoothly curved or slanted boundaries with stairsteps. The desire to incorporate realistic boundaries into plasma simulations is motivated by a host of situations in which proper representation of the boundary shape is expected to be critical. Our approach to solving this problem is to design electromagnetic particle codes based on the use of unstructured grids. The arbitrary connectivity of unstructured grids provides the flexibility to place nodes wherever needed to fit the most complex boundary shapes. The most significant problems that must be addressed as a result of this strategy are: grid generation, field solution, and particle tracking. Our solutions to these problems, along with a few preliminary results, are presented in this paper.

  Abstract
  The most widely used computational model of collisionless plasmas is the Lagrangian-Eulerian hybrid technique known as particle-in-cell or PIC. In the electromagnetic version, [...]

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• Adaptive remeshing for transient problems with moving bodies

  R. Lohner

  (1989). 11th International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 323. Springer, Berlin, Heidelberg

  
  

  Abstract

  The accurate simulation of time-dependent compressible flows with moving bodies has been an outstanding goal for a long time. Several major capabilities are required to simulate efficiently this class of problems: a) Flow solvers that can handle moving frames of reference, b) high-order, monotonicity preserving schemes, c) a consistent integration scheme for the rigid body motion, and d) fast regridding capabilities. It is also convenient to incorporate an adaptive refinement capability for the flow domain in order to reduce the overall CPU-cost of the algorithm.

  Abstract
  The accurate simulation of time-dependent compressible flows with moving bodies has been an outstanding goal for a long time. Several major capabilities are required to simulate [...]

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• An unstructured-grid based volume-of-fluid method for extreme wave and freely-floating structure interactions

  C. Yang, R. Lohner, H. Lu

  Journal of Hydrodynamics (2006). Vol. 18 (1), pp. 405-412

  
  

  Abstract

  A Volume of Fluid (VOF) technique has been further developed and coupled with an incompressible Euler/Navier Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and a LNG carrier with full or partially filled tanks. The present implementation follows the classic VOF implementation for the liquid-gas system, considering only the liquid phase. Extrapolation algorithms are used to obtain velocities and pressures in the gas region near the free surface. An arbitrary Lagrangian-Eulerian (ALE) frame of reference is used. The mesh is moved in such a way as to minimize the distortion of the mesh due to body movement. The incompressible Euler/Navier-Stokes equations are solved using projection schemes and a finite element method on unstructured grids, and the free surface is captured by the VOF method. The computer code developed based on the method described above is used in this study to simulate a numerical seakeeping tank, where the waves are generated by the sinusoidal excitation of a piston paddle, and a freely-floating LNG carrier with full or partially filled tanks moves in response to the waves. Both head sea and oblique sea are considered in the simulation. Highly nonlinear wave-body interactions, such as green water on deck and sloshing, have been modeled successfully.

  Abstract
  A Volume of Fluid (VOF) technique has been further developed and coupled with an incompressible Euler/Navier Stokes solver operating on adaptive, unstructured grids to simulate [...]

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• Improving the speed and accuracy of projection-type incompressible flow solvers

  R. Lohner, C. Yang, J. Cebral, F. Camelli, O. Soto, J. Waltz

  Comput. Methods Appl. Mech. Engrg., (2006). 195 (23-24), pp. 3087-3109

  
  

  Abstract

  Superseding so-called first-generation incompressible flow solvers of the projection type (based on Taylor–Galerkin advection, second-order pressure damping and element-based data structures), the current, second-generation solvers (based on high-order upwind advection, fourth-order pressure damping and edge-based data structures) have now been in use for half a decade and have proven remarkably robust and efficient for many large-scale problems. In order to achieve higher accuracy and speed, these solvers have recently been enhanced in a variety of ways: (a) substepping for advection, (b) implicit treatment of advective terms via SGS and GMRES-LU-SGS iterative solvers, (c) fully implicit, time-accurate advancement of pressure and velocities, and (d) linelet preconditioning for the pressure-Poisson equation. The combined effect of these third-generation improvements leads to speedups of the order of O(1:5−1:10), with similar or even better temporal accuracy, as demonstrated on a variety of academic and industrial problems.

  Abstract
  Superseding so-called first-generation incompressible flow solvers of the projection type (based on Taylor–Galerkin advection, second-order pressure damping and element-based [...]

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• Applications of the method of flux-corrected transport to generalized meshes

  R. Lohner, G. Patnaik

  (1986). Tenth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 264. Springer, Berlin, Heidelberg

  
  

  Abstract

  A new technique for numerical solution of fluid equations has been developed by combining the Finite-Element Methods with the method of Flux-Corrected Transport. The resulting hybrid method, called FEM-FCT, is useful for problems involving steady and unsteady transonic and supersonic flow irregular geometries. The main computational advance grows out of the need to find a prescription for limiting fluxes through the sides of a triangular or other nonquadrilateral zone when arbitrarily many zones may meet at a given vertex.

  Abstract
  A new technique for numerical solution of fluid equations has been developed by combining the Finite-Element Methods with the method of Flux-Corrected Transport. The resulting [...]

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• A hybrid Cartesian grid and gridless method for compressible flows

  H. Luo, J. Baum, R. Lohner

  Journal of Computational Physics (2006). Vol. 214 (2), pp. 618-632

  
  

  Abstract

  A hybrid Cartesian grid and gridless method is presented to compute unsteady compressible flows for complex geometries. In this method, a Cartesian grid is used as baseline mesh to cover the computational domain, while the boundary surfaces are addressed using a gridless method. This hybrid method combines the efficiency of a Cartesian grid method and the flexibility of a gridless method for the complex geometries. The developed method is used to compute a number of test cases to validate the accuracy and efficiency of the method. The numerical results obtained indicate that the use of this hybrid method leads to a significant improvement in performance over its unstructured grid counterpart for the time-accurate solution of the compressible Euler equations. An overall speed-up factor of about eight and a saving in storage requirements about one order of magnitude for a typical three-dimensional problem in comparison with the unstructured grid method are demonstrated.

  Abstract
  A hybrid Cartesian grid and gridless method is presented to compute unsteady compressible flows for complex geometries. In this method, a Cartesian grid is used [...]

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• A hybrid building‐block and gridless method for compressible flows

  H. Luo, J. Baum, R. Lohner

  Int. J. Numer. Meth. Fluids (2006). Vol. 59 (4), pp. 459-474

  
  

  Abstract

  A hybrid building‐block Cartesian grid and gridless method is presented to compute unsteady compressible flows for complex geometries. In this method, a Cartesian mesh based on a building‐block grid is used as a baseline mesh to cover the computational domain, while the boundary surfaces are represented using a set of gridless points. This hybrid method combines the efficiency of a Cartesian grid method and the flexibility of a gridless method for the complex geometries. The developed method is used to compute a number of test cases to validate the accuracy and efficiency of the method. The numerical results obtained indicate that the use of this hybrid method leads to a significant improvement in performance over its unstructured grid counterpart for the time‐accurate solution of the compressible Euler equations. An overall speed‐up factor from six to more than one order of magnitude and a saving in storage requirements up to one order of magnitude for all test cases in comparison with the unstructured grid method are demonstrated.

  Abstract
  A hybrid building‐block Cartesian grid and gridless method is presented to compute unsteady compressible flows for complex geometries. In this method, a Cartesian mesh based [...]

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• An unstructured-grid based volume-of-fluid method for extreme wave and freely-floating structure interactions

  C. Yang, R. Lohner, H. Lu

  Journal of Hydrodynamics (2006). Vol. 18 (3), pp. 415-422

  
  

  Abstract

  A Volume of Fluid (VOF) technique has been further developed and coupled with an incompressible Euler/Navier Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and a LNG carrier with full or partially filled tanks. The present implementation follows the classic VOF implementation for the liquid-gas system, considering only the liquid phase. Extrapolation algorithms are used to obtain velocities and pressures in the gas region near the free surface. An arbitrary Lagrangian-Eulerian (ALE) frame of reference is used. The mesh is moved in such a way as to minimize the distortion of the mesh due to body movement. The incompressible Euler/Navier-Stokes equations are solved using projection schemes and a finite element method on unstructured grids, and the free surface is captured by the VOF method. The computer code developed based on the method described above is used in this study to simulate a numerical seakeeping tank, where the waves are generated by the sinusoidal excitation of a piston paddle, and a freely-floating LNG carrier with full or partially filled tanks moves in response to the waves. Both head sea and oblique sea are considered in the simulation. Highly nonlinear wave-body interactions, such as green water on deck and sloshing, have been modeled successfully.

  Abstract
  A Volume of Fluid (VOF) technique has been further developed and coupled with an incompressible Euler/Navier Stokes solver operating on adaptive, unstructured grids to simulate [...]

  • 0
  •  read