Johns Hopkins Turbulence Database

Spatial and Temporal Methods

Database Spatial Operator Options:

Field: Returns field values of the specified Physical Variable (e.g. velocity, pressure, temperature, density, etc.) at specified points and time.

Gradient: Returns first order derivatives in three directions of the specified Physical Variable.

Hessian: Returns all second order derivatives in three directions of the specified Physical Variable.


Database Spatial Methods Options:

Options for Spatial Operator=Field:

none: No space interpolation (value at the datapoint closest to each coordinate value)

lag4: 4th-order Lagrange Polynomial interpolation along each spatial direction [See Ref. 1, Appendix C.1] DOI

lag6: 6th-order Lagrange Polynomial interpolation along each spatial direction [See Ref. 1, Appendix C.1] DOI

lag8: 8th-order Lagrange Polynomial interpolation along each spatial direction [See Ref. 1, Appendix C.1] DOI

m1q4: Splines with smoothness 1 (3rd order) over 4 data points. [See Ref. 2, Appendix 3] DOI

m2q8: Splines with smoothness 2 (5th order) over 8 data points. [See Ref. 2, Appendix 3] DOI


Options for Spatial Operator=Gradient:

fd4noint: No interpolation (value of the 4th order finite-difference evaluations at the datapoint closest to each coordinate value is returned) [See Ref. 1, Appendix C.1] DOI

fd6noint: No interpolation (value of the 6th order finite-difference evaluations at the datapoint closest to each coordinate value is returned) [See Ref. 1, Appendix C.1] DOI

fd8noint: No interpolation (value of the 8th order finite-difference evaluations at the datapoint closest to each coordinate value is returned) [See Ref. 1, Appendix C.1] DOI

fd4lag4: 4th-order Lagrange Polynomial interpolation in each direction, of the 4th-order finite difference values on the grid. [See Ref. 1, Appendix C.1] DOI

m1q4: Splines with smoothness 1 (3rd order) over 4 data points. [See Ref. 2, Appendix 3] DOI

m2q8: Splines with smoothness 2 (5th order) over 8 data points. [See Ref. 2, Appendix 3] DOI


Options for Spatial Operator=Hessian:

fd4noint: No interpolation (value of the 4th order finite-difference evaluations at the datapoint closest to each coordinate value is returned) [See Ref. 1, Appendix C.1] DOI

fd6noint: No interpolation (value of the 6th order finite-difference evaluations at the datapoint closest to each coordinate value is returned) [See Ref. 1, Appendix C.1] DOI

fd8noint: No interpolation (value of the 8th order finite-difference evaluations at the datapoint closest to each coordinate value is returned) [See Ref. 1, Appendix C.1] DOI

m2q8: Splines with smoothness 2 (5th order) over 8 data points [See Ref. 2, Appendix 3] DOI


Database temporal Methods Options:

For all variables and derivatives listed above, the two options are:

none: No interpolation (the value at the closest stored time will be returned).

pchip: Piecewise Cubic Hermite Interpolation Polynomial method is used, in which the value from the two nearest time points is interpolated at time t using Cubic Hermite Interpolation Polynomial, with centered finite difference evaluation of the end-point time derivatives (i.e. a total of four temporal points is used). [See Ref. 1, Appendix D] DOI