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The unsteady stream function-vorticity formulation is used to solve the governing equations.
One-field formulation is used to solve the flow, energy and species equations in the framework of the front tracking method, with suitable jump conditions at the interface.
Because in MBS applications the generalized forces can be highly nonlinear and can depend on the velocities, a state space formulation is used to solve the eigenvalue problem.
An alternative vector potential formulation is used to solve the Navier Stokes (N S) equations in 3D incompressible viscous flow problems with and without through-flow boundaries.
A Green Element numerical formulation is used to solve the time-dependent nonlinear one-dimensional counter-current spontaneous imbibition diffusion equation in which water enters a water wet rock spontaneously while oil escapes by flowing in the opposite direction.
In this paper, a first-order system least squares finite element formulation is used to solve the nonlinear system of model equations using different iteration techniques, including an approach where the equations are fully coupled and two other approaches in which the equations are decoupled.
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In V-REP, the following DLS formulation is used to solve IK problems.
A Bubnov-Galerkin formulation is used to solve an elliptic grid generation system by using linear and quadratic isoparametric elements.
The following stepwise procedure of GRA optimization is used to solve the current formulation (Deng 1989).
Two-space genetic algorithm is used to solve the problem formulation.
Proposed formulations are used to solve three hypothetical test examples of different scales and the results are presented and compared.
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