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In [[thermodynamics]], '''dissipation''' is the result of an [[irreversible process]] that takes place in homogeneous [[Thermodynamic system|thermodynamic systems]]. A dissipative process is a process in which [[energy]] ([[Internal energy|internal]], bulk flow [[Kinetic energy|kinetic]], or system [[Potential energy|potential]]) is [[Energy transformation|transformed]] from some initial form to some final form; the capacity of the final form to do [[mechanical work]] is less than that of the initial form. For example, [[Heat Transfer|heat transfer]] is dissipative because it is a transfer of internal energy from a hotter body to a colder one. Following the [[second law of thermodynamics]], the [[entropy]] varies with [[temperature]] (reduces the capacity of the combination of the two bodies to do mechanical work), but never decreases in an isolated system.

In [[thermodynamics]], '''dissipation''' is the result of an [[irreversible process]] that takes place in homogeneous [[Thermodynamic system|thermodynamic systems]]. A dissipative process is a process in which [[energy]] ([[Internal energy|internal]], bulk flow [[Kinetic energy|kinetic]], or system [[Potential energy|potential]]) is [[Energy transformation|transformed]] from some initial form to some final form; the capacity of the final form to do [[mechanical work]] is less than that of the initial form. For example, [[Heat Transfer|heat transfer]] is dissipative because it is a transfer of internal energy from a hotter body to a colder one. Following the [[second law of thermodynamics]], the [[entropy]] varies with [[temperature]] (reduces the capacity of the combination of the two bodies to do mechanical work), but never decreases in an isolated system.

 

In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. A dissipative process is a process in which energy (internal, bulk flow kinetic, or system potential) is transformed from some initial form to some final form; the capacity of the final form to do mechanical work is less than that of the initial form. For example, heat transfer is dissipative because it is a transfer of internal energy from a hotter body to a colder one. Following the second law of thermodynamics, the entropy varies with temperature (reduces the capacity of the combination of the two bodies to do mechanical work), but never decreases in an isolated system.

In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. A dissipative process is a process in which energy (internal, bulk flow kinetic, or system potential) is transformed from some initial form to some final form; the capacity of the final form to do mechanical work is less than that of the initial form. For example, heat transfer is dissipative because it is a transfer of internal energy from a hotter body to a colder one. Following the second law of thermodynamics, the entropy varies with temperature (reduces the capacity of the combination of the two bodies to do mechanical work), but never decreases in an isolated system.

A particular occurrence of a dissipative process cannot be described by a single individual Hamiltonian formalism. A dissipative process requires a collection of admissible individual Hamiltonian descriptions, exactly which one describes the actual particular occurrence of the process of interest being unknown. This includes friction, and all similar forces that result in decoherency of energy—that is, conversion of coherent or directed energy flow into an indirected or more isotropic distribution of energy.

A particular occurrence of a dissipative process cannot be described by a single individual Hamiltonian formalism. A dissipative process requires a collection of admissible individual Hamiltonian descriptions, exactly which one describes the actual particular occurrence of the process of interest being unknown. This includes friction, and all similar forces that result in decoherency of energy—that is, conversion of coherent or directed energy flow into an indirected or more isotropic distribution of energy.

In [[computational physics]], numerical dissipation (also known as "numerical diffusion") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. When the pure [[advection]] equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way analogous to a diffusional process. Such a method is said to contain 'dissipation'. In some cases, "artificial dissipation" is intentionally added to improve the [[numerical stability]] characteristics of the solution.<ref>Thomas, J.W. Numerical Partial Differential Equation: Finite Difference Methods. Springer-Verlag. New York. (1995)</ref>

In [[computational physics]], numerical dissipation (also known as "numerical diffusion") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. When the pure [[advection]] equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way analogous to a diffusional process. Such a method is said to contain 'dissipation'. In some cases, "artificial dissipation" is intentionally added to improve the [[numerical stability]] characteristics of the solution.<ref>Thomas, J.W. Numerical Partial Differential Equation: Finite Difference Methods. Springer-Verlag. New York. (1995)</ref>

 

In computational physics, numerical dissipation (also known as "numerical diffusion") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. When the pure advection equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way analogous to a diffusional process. Such a method is said to contain 'dissipation'. In some cases, "artificial dissipation" is intentionally added to improve the numerical stability characteristics of the solution.

In computational physics, numerical dissipation (also known as "numerical diffusion") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. When the pure advection equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way analogous to a diffusional process. Such a method is said to contain 'dissipation'. In some cases, "artificial dissipation" is intentionally added to improve the numerical stability characteristics of the solution.