Not enough information for a meaningful answer - and do you 'assimilation' or 'simulation', or perhaps 'assimilation' / 'acquisition'.

Some context would be helpful - if you are doing a 'one-off' you could use a desktop GIS application like ArcMap or QGIS, ( or SAGA, Whitebox, GRASS ... ), if you are doing a few, you could use the 'model builder' tools in those apps. If you are doing a more massive amount, you could use Python scripts to call the functions of the programs or use GDAL scripts, or even 'R'. You can write the scripts in the GIS app's editor, or stand alone in a development environment, or in a Jupityr Notebook. All of these have extensive processing libraries, some very specific to a particular domain ( like archeology or hydrology ), and there are stand alone tools.

It depends a great deal on your own environment, knowledge, skills, and experience, too. And if you expect others to use the same tool chain / pipeline.

To be clear, while you can increase the apparent resolution of raster data, in general in any raster transformation information can be lost and artifacts introduced. For instance if you are doing something very custom, and know Java really well, you might use https://jblindsay.github.io/ghrg/Whitebox/

There are also many platforms with their sensors, which dictate the sorts of processing that can be accomplished.

The more specific you are, the higher probability someone will help you.

Behnam Khorrami If you assimilate atmosphere variables, GSI or DART may help you. If you assimilate land variables, LIS(NASA) may help you.

Your question appears very vague. You say increase the resolution of satellite data and at the same time you are saying "some kind of downscaling". How come both are possible. If you are saying that you want to use model output along with satellite data then I suggest you to use DIVA for arriving at a good output with your desired resolution. The software is freely available with GHER web site.