- Email: [email protected]
Papers from the third international workshop on numerical simulation of viscoelastic flows
Journal of Non -Newtonian Fluid Mechanics, 16 (1984) 1-2 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
1
Editorial
PAPERS FROM THE THIRD INTERNATIONAL NUMERICAL SIMULATION OF VISCOELASTIC
WORKSHOP FLOWS
ON
Luke Morey, Vermont, NE, U.S.A., June 5- 8, 1983
Computer-aided analysis of complex flows of viscoelastic fluids has been an active area of non-Newtonian fluid mechanics since the early seventies and has now been the subject of three international workshops aimed at the considerable numerical and rheological problems necessary for successful calculation of these flows. The last meeting was held in June, 1983 at Lake Morey, Vermont. The papers in this special issue are not a complete proceedings of this meeting, but do reasonably represent the state of the field up to this past summer. There were also several papers at the Vermont meeting that dealt with the experimental facts that we are trying to compute; these have not been included here in order to maintain the focus on the numerical problems. In the last two years, researchers have expanded numerical formulations to handle more complicated differential and integral constitutive equations. These efforts have led to new understanding of the relationship between fluid rheology and the convergence difficulties that have plagued computations. Also, several investigations have focused on the structure of the solutions for more commonly used constitutive equations and have connected the loss of convergence of the numerical scheme with increasing Deborah number to”‘the loss of solution for the discretized equation set and possibly the original mathematical problem. The first steps toward mathematical classification $6 con@lete sets of equations for velocity and stress have been carried out andi; promise insights into the loss of accuracy presently seen for calculations at high Deborah number. An important outcome of this workshop, like it predecessors, is a clearer understanding of the significant problems facing us as we attempt to develop further the numerical capability for calculating viscoelastic flows. It is still not clear whether or not the numerical limitations are due to pathological behavior in commonly used constitutive equations such as the convected Maxwell model or whether the limits reflect changes in flow structure to three dimensions or time-dependence, or possibly an inadequate ability to resolve regions of rapid change adequately. Important numerical problems to be addressed are then developing of viable transient techniques, local mesh 0377-0257/84/$03.00
0 1984 Elsevier Science Publishers B.V.
2 refinement techniques, and also quantifying the roles of flow geometry, constitutive equation, and boundary conditions on the numerical solutions. The experimentalists do not get off easily either. We need more and better measurements of both stress and velocity fields for well characterized fluids that can be used for comparison with calculations. Measurements of flow transitions and of time-dependent flows are badly needed as are additional studies of the flow near solid boundaries. Finally, analytical solutions for model test problems and solutions for flow regions such as the sharp corner in the contraction problem would be very valuable. In addition to the sudden contraction flow which has been the standard test problem for the first three workshops, it was decided that for the next workshop we should add the problem of viscoelastic flow around a sphere. This will provide a test problem in which there are no sharp corners to induce stress singularities which seem to cause so many problems in the abrupt contraction flow. Both experimental and computational results are needed on this problem. A standard set of problem specifications will be available from Professor M.J. Crochet at University of Louvain, Belgium; he is organizing the next workshop which is scheduled for June, 1985 in Belgium. ROBERT C. ARMSTRONG ROBERT A. BROWN Massachusetts Institute of Technology BRUCE CASWELL Brown University
1
Editorial
PAPERS FROM THE THIRD INTERNATIONAL NUMERICAL SIMULATION OF VISCOELASTIC
WORKSHOP FLOWS
ON
Luke Morey, Vermont, NE, U.S.A., June 5- 8, 1983
Computer-aided analysis of complex flows of viscoelastic fluids has been an active area of non-Newtonian fluid mechanics since the early seventies and has now been the subject of three international workshops aimed at the considerable numerical and rheological problems necessary for successful calculation of these flows. The last meeting was held in June, 1983 at Lake Morey, Vermont. The papers in this special issue are not a complete proceedings of this meeting, but do reasonably represent the state of the field up to this past summer. There were also several papers at the Vermont meeting that dealt with the experimental facts that we are trying to compute; these have not been included here in order to maintain the focus on the numerical problems. In the last two years, researchers have expanded numerical formulations to handle more complicated differential and integral constitutive equations. These efforts have led to new understanding of the relationship between fluid rheology and the convergence difficulties that have plagued computations. Also, several investigations have focused on the structure of the solutions for more commonly used constitutive equations and have connected the loss of convergence of the numerical scheme with increasing Deborah number to”‘the loss of solution for the discretized equation set and possibly the original mathematical problem. The first steps toward mathematical classification $6 con@lete sets of equations for velocity and stress have been carried out andi; promise insights into the loss of accuracy presently seen for calculations at high Deborah number. An important outcome of this workshop, like it predecessors, is a clearer understanding of the significant problems facing us as we attempt to develop further the numerical capability for calculating viscoelastic flows. It is still not clear whether or not the numerical limitations are due to pathological behavior in commonly used constitutive equations such as the convected Maxwell model or whether the limits reflect changes in flow structure to three dimensions or time-dependence, or possibly an inadequate ability to resolve regions of rapid change adequately. Important numerical problems to be addressed are then developing of viable transient techniques, local mesh 0377-0257/84/$03.00
0 1984 Elsevier Science Publishers B.V.
2 refinement techniques, and also quantifying the roles of flow geometry, constitutive equation, and boundary conditions on the numerical solutions. The experimentalists do not get off easily either. We need more and better measurements of both stress and velocity fields for well characterized fluids that can be used for comparison with calculations. Measurements of flow transitions and of time-dependent flows are badly needed as are additional studies of the flow near solid boundaries. Finally, analytical solutions for model test problems and solutions for flow regions such as the sharp corner in the contraction problem would be very valuable. In addition to the sudden contraction flow which has been the standard test problem for the first three workshops, it was decided that for the next workshop we should add the problem of viscoelastic flow around a sphere. This will provide a test problem in which there are no sharp corners to induce stress singularities which seem to cause so many problems in the abrupt contraction flow. Both experimental and computational results are needed on this problem. A standard set of problem specifications will be available from Professor M.J. Crochet at University of Louvain, Belgium; he is organizing the next workshop which is scheduled for June, 1985 in Belgium. ROBERT C. ARMSTRONG ROBERT A. BROWN Massachusetts Institute of Technology BRUCE CASWELL Brown University