| 51. |
- Ghader, Sarmad, et al.
(författare)
-
Well-posed boundary conditions for the shallow water equations
- 2013
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We derive well-posed boundary conditions for the two-dimensional shallow water equations by using the energy method. Both the number and the type of boundary conditions are presented for subcritical and supercritical flows on a general domain. Then, as an example, the boundary conditions are discussed for a rectangular domain.
|
|
| 52. |
- Ghasemi, Fatemeh, et al.
(författare)
-
Coupling requirements for multi-physics problems
- 2016
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We consider two hyperbolic systems onfirst order form of different size posed on two domains. Our ambition is to derive general conditions for when the two systems can and cannot be coupled.The adjoint equations are derived and well-posedness of the primal and dual problems are discussed. By applying the energy method, interface conditions for the primal and dual problems are derived such that the continuous problems are well posed.The equations are discretized using a high order finite difference method on summation-by-parts form and the interface conditions are imposed weakly in a stable way, using penalty formulations. It is shown that one specific choice of penalty matrices leads to a dual consistent scheme and superconverging functionals.By considering an example, it is shown that the correct physical coupling conditions are contained in the set of well posed coupling conditions. It is also shown that the correct convergence rates are obtained for both the solutions and functionals.
|
|
| 53. |
- Ghasemi Zinatabadi, Fatemeh, 1988-, et al.
(författare)
-
An Energy Stable Coupling Procedure for the Compressible and Incompressible Navier-Stokes Equations
- 2019
-
Ingår i: Journal of Computational Physics. - Linköping : Linköping University Electronic Press. - 0021-9991 .- 1090-2716. ; 396, s. 280-302
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The coupling of the compressible and incompressible Navier-Stokes equations is considered. Our ambition is to take a first step towards a provably well posed and stable coupling procedure. We study a simplified setting with a stationary planar interface and small disturbances from a steady background ow with zero velocity normal to the interface.The simplified setting motivates the use of the linearized equations, and we derive interface conditions such that the continuous problem satisfy an energy estimate. The interface conditions can be imposed both strongly and weakly. It is shown that the weak and strong interface imposition produce similar continuous energy estimates.We discretize the problem in time and space by employing finite difference operators that satisfy a summation-by-parts rule. The interface and initial conditions are imposed weakly using a penalty formulation. It is shown that the results obtained for the weak interface conditions in the continuous case, lead directly to stability of the fully discrete problem.
|
|
| 54. |
- Ghasemi Zinatabadi, Fatemeh, 1988-, et al.
(författare)
-
On conservation and dual consistency for summation-by-parts based approximations of parabolic problems
- 2019
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We consider the coupling of parabolic problems discretized using difference operators on summation-by-parts (SBP) form with interface conditions imposed weakly. In, it was shown that conservation and dual consistency are equivalent concepts for linear conservation laws. Here, we show that these concepts are equivalent also for symmetric or symmetrizable parabolic problems, exemplified by the heat equation. We rewrite the heat equation as first order system as in the local discontinuous Galerkin method and show the equivalence of dual consistency and conservation for both the first and second order forms.
|
|
| 55. |
- Ghasemi Zinatabadi, Fatemeh, 1988-, et al.
(författare)
-
The Relation Between Primal and Dual Boundary Conditions for Hyperbolic Systems of Equations
- 2019
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we study boundary conditions for linear hyperbolic systems of equations and the corresponding dual problems. In particular, we show that the primal and dual boundary conditions are related by a simple scaling relation. It is also shown that the weak dual problem can be derived directly from the weak primal problem.Based on the continuous analysis, we discretize and perform computations with a high-order finite difference scheme on summation-by-parts form with weak boundary conditions. It is shown that the results obtained in the continuous analysis lead directly to stability results for the primal and dual discrete problems. Numerical experiments corroborate the theoretical results.
|
|
| 56. |
- Ghosh, Arpan, et al.
(författare)
-
A Two Dimensional Model of the Thin Laminar Wall of a Curvilinear Flexible Pipe
- 2018
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We present a two dimensional model describing the elastic behaviour of the wall of a curved pipe to model blood vessels in particular. The wall has a laminate structure consisting of several anisotropic layers of varying thickness and is assumed to be much smaller in thickness than the radius of the vessel which itself is allowed to vary. Our two-dimensional model takes the interaction of the wall with the surrounding material and the fluid flowing inside into account and is obtained via a dimension reduction procedure. The curvature and twist of the vessel axis as well as the anisotropy of the laminate wallpresent the main challenges in applying the dimension reduction procedure so plenty of examples of canonical shapes of vessels and their walls are supplied with explicit systems of dierential equations at the end.
|
|
| 57. |
- Gorgorió, Núria, et al.
(författare)
-
Fundamental Mathematical Knowledge : progressing its specification
- 2019
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we elaborate on the notion of Fundamental Mathematical Knowledge (FMK) which we understand as the minimum mathematical content knowledge essential to enter a degree in primary teacher education. We propose that FMK can be assessed in terms of competency in different areas of primary mathematics. The aim of this paper is to present our on-going work to specify FMK based on the common content of mathematics as a primary school subject in Catalonia, England, Finland, and Sweden.
|
|
| 58. |
- Hajizadeh, Roghayeh, 1986-, et al.
(författare)
-
Coordination of vehicles in urban snow removal
- 2021
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Snow removal is an unavoidable problem in Nordic countries like Sweden. A number of streets in a city need to be cleared of snow by a limited number of vehicles. The problem can be formulated as a very large mixed integer programming model, which is practically unsolvable. In order to find a feasible solution, first we break done the work into smaller parts, one for each vehicle. To find which streets a vehicle shall take care of, we solve a weighted k-Chinese postman problem. Based on the allocation obtained, we consider snow removal problems for single vehicles, where details such as turning penalties and precedences are included. These problems can be reformulated to asymmetric traveling salesman problems in extended graphs, and we have a heuristic for finding feasible solution of those. In this paper, we discuss combined solution approaches and coordination of the vehicles to find a feasible solution for the whole original problem including all details. We use an iterative procedure to combine the tours, based on the tools mentioned above, and a procedure for constructive coordination of the tours. We also have new improvement procedures for the combined solution. We have implemented the methods and applied them to real life city networks. The numerical results show that the methods obtain feasible tours for large problems within a reasonable time.
|
|
| 59. |
- Hajizadeh, Roghayeh, 1986-, et al.
(författare)
-
In search of good relaxations for the urban snow removal problem
- 2023
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Snow removal is, in Sweden, an infrequently occurring challenge. Doing the snow removal more efficiently could give much benefits for society. Since the amounts of snow vary a lot from day to day, and from year to year, fixed plans are not the best. Optimization of the snow removal tours could save much money. In this paper, we study the multi-vehicle urban snow removal problem from a mixed integer programming perspective. It is a very hard problem, and obtaining the exact optimum seems to be out of reach. Therefore, we study relaxations of the problem. Our goal is simply to find the best bounds for the optimal objective function value that is possible in limited time. We present some promising possibilities, verified by extensive computational tests.
|
|
| 60. |
- Hajizadeh, Roghayeh, 1986-, et al.
(författare)
-
Lagrangian relaxation for the urban snow removal problem
- 2023
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Snow removal problem in cities is a challenging task in Nordic countries. The problem is finding optimal tours for a certain number of vehicles with some circumstances in order to clear a number of streets in a city. We have formulated the urban snow removal problem as a time-indexed mixed integer linear programming model which is huge and complicated. In our previous work, we studied the model and its different relaxations which show that the problem is not solvable in practice. Since the problem has many sets of constraints with complicated structures, relaxing them with Lagrangian relaxation might be beneficial. In this paper, we discuss different possibilities of relaxing sets of constraints and develop a Lagrangian heuristic which consists of a suitable Lagrangian relaxation of the problem, a subgradient optimization method for solving the Lagrangian dual, and procedures for obtaining feasible solutions. The heuristic has been implemented and applied to artificial and real life city networks. The results show that the bounds have been improved.
|
|
