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Conservation Equations
Published in Krishnan Murugesan, Modeling and Simulation in Thermal and Fluids Engineering, 2023
This type of boundary condition is also called boundary condition of first kind and this corresponds to a situation for which the temperature at the boundary is known and is assumed that boundary is maintained at a constant fixed temperature. For example, the surface over which boiling or condensation takes place can be treated as a boundary condition of first kind. For one-dimensional heat conduction along the x-direction, the boundary conditions at two points, x=0 and x=L, have to be specified. For steady heat conduction, the Dirichlet boundary condition is specified as @x=0,T0=Tw
A comparative study for resistance prediction using different RANS solvers
Published in C. Guedes Soares, T.A. Santos, Trends in Maritime Technology and Engineering Volume 1, 2022
M.M. Rahaman, N.M.G. Zakaria, M. Mostafiz, H. Islam
In this study, for boundary conditions, the bottom, and the sides of the simulation domain are treated as local symmetry planes. The symmetry boundary condition is defined as a mirror surface, where fluxes and normal components of all variables across the symmetry are set to zero. The symmetry in this case works as a non-reflecting boundary condition which ignores interaction of the flow field with the sides. The pressure boundary condition at the inlet applies a zero-gradient condition from the patch internal field onto the patch faces (zeroGradient: Neumann boundary condition), the outlet boundary supplies a fixed value constraint (fixedValue: Dirichlet boundary condition). As for velocity, the inlet is set as a fixed value constraint (fixedValue), and the outlet is set to be a generic outflow condition with zero return inflow (inletOutlet). Values for the turbulence parameters are set following the Reynolds number (Labanti et al., 2016).
Simulation of Biological Processes
Published in Robert M. Peart, R. Bruce Curry, Agricultural Systems Modeling and Simulation, 2018
James W. Jones, Joep C. Luyten
This system of equations can be simulated if initial conditions ωi(0) and boundary conditions i(t), O(t) are known for i = 1, 2, …, n and t > 0. Initial conditions refer to the values of all state variables at the start of the simulation, usually at time t = 0; they are required for simulating the behavior of a model. As an example, if a system has two state variables x(t) and y(t), then x(0) and y(0) must be specified in order to simulate system behavior for t > 0. Boundary conditions refer to values of variables at the boundaries of a system. Boundary conditions may refer to flows across the system boundary or to known values of intensive variables at the boundary. Values of boundary conditions must be specified for all time to be simulated.
Utilising physics-informed neural networks for optimisation of diffusion coefficients in pseudo-binary diffusion couples
Published in Philosophical Magazine, 2023
Hemanth Kumar, Neelamegan Esakkiraja, Anuj Dash, Aloke Paul, Saswata Bhattacharyya
For the special case in which only two components develop the diffusion profile in the interdiffusion zone, such as in CB and PB diffusion couple experiments, the PDE-constrained optimisation procedure is formulated as: where is the composition field of the independent diffusing species, is the interdiffusion coefficient, and are the intrinsic diffusion coefficients at the K-plane. Note that there is no restriction on the type of boundary condition used – one can use Dirichlet, Neumann, periodic, or mixed boundary conditions. In the case of CB, we consider the composition variables and , while in the case of PB, we use the modified composition variables, and . The contributions to the composite loss function are: Here, and . Thus,
Undergraduate students' difficulties with boundary conditions for the diffusion equation
Published in International Journal of Mathematical Education in Science and Technology, 2022
Sofie Van den Eynde, Johan Deprez, Martin Goedhart, Mieke De Cock
The initial condition describes the state of the system at the beginning (t = 0). Boundary conditions refer to the conditions physical quantities must satisfy at the boundary of the system. In this study we focus on boundary conditions of the form , which specify the flux, which in this context is the particle flow, through the boundary. More specifically, we consider a closed tube, so no particles can pass the boundary. Mathematically, this is described by the following boundary conditions: and .
Recent Features and Industrial Applications of the Hybrid SPH-FE Method
Published in International Journal of Computational Fluid Dynamics, 2021
Paul Groenenboom, Bruce Cartwright, Damian McGuckin
Periodic boundary conditions are mathematical conditions that can be placed on the boundary of a computational domain to mimic the behaviour of a larger or infinite domain. For Eulerian types of CFD, this may be accomplished by equating the inflow at one boundary to the outflow at the opposing boundary. For SPH, an additional requirement is that particles that exit at one boundary are entering at the opposite boundary at the same conditions, and that the neighbourhood of particles near such boundaries is extended to include the opposite boundary as well. An enhancement is the translating periodic boundary condition (TPBC), where the upstream and downstream boundaries can be assigned to move according to some arbitrary function, or to a selected FE node. This enables the study of a structure as it moves with respect to the fluid without modelling the entire distance that would be covered during the entire simulation. An optional feature of the translating periodic boundary is that the upstream conditions are those of a fluid at-rest, and not the disturbed downstream conditions in the case where a structure has interacted with the fluid in some way. In this case, the conditions and locations of the SPH particles as they exit the translating downstream boundary are reset to their (original) at-rest conditions and locations on re-entering the upstream periodic boundary condition. This feature allows recycling of the particles from the spray in the downstream region for an object interacting with the free surface as particles in the undisturbed fluid in front of the object. Figures 2 and 3 below sketch the application of the TPBC in horizontal direction; the damping zone may be included to mitigate any disturbance due to the interaction between the fluid and an immersed structure.